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HI 

PHILOSOPHICAL 

TRANSACTIONS 



OF THE 



ROYAL SOCIETY OF LONDON 



SERIES A. 



CONTAINING 1'APEES OF A MATHEMATICAL OE PHYSICAL CHAEACTEE. 



VOL. 205. 



LONDON : 

PRINTED BY HARRISON AND SONS, ST. MARTIN'S LANE, W.C., 

iit ^rbinarg to |jis gjajtstg. 

MAY, 1906. 




Q 
f I 



CONTENTS, 

(A) 
VOL. 205. 



List of Illustrations page v 

Advertisement . vii 



I. On the Normal Series satisfying Linear Differential Equations. By E. CUNNING- 

HAM, B.A., Fellow of St. John's College, Cambridge. Communicated by 
Dr. D. H. F. BAKER, F.R.S page 1 

II. Memoir on the Theory of the Partitions of Numbers. Part III. By P. A. 

MACMAHON, Major P. A., Se.D., F.R.S 37 

III. Atmospheric Electricity in High Latitudes. By GEORGE C. SIMPSON, B.Sc. 

(1851 Exhibition Scholar of the University of Manchester). Communicated 
by ARTHUR SCHUSTER, F.R. S. (51 

IV. The Halogen Hydrides as Conducting Solvents. Part I. The. Vapour 

Pressures, Densities, Surface Energies and Viscosities of the. Pure Solvents. 
Part II. The Conductivity and Molecular Weights of Dissolved Substances. 
Part II f. The Transport Numbers of. Certain Dissolved Substances. 
Part IV. The Abnormal Variation of Molecular Conductivity, etc. By 
B. D. STEELE, D.Sc., D. MC!NTOSH, M.A., D.Sc., and E. H. ARCHIBALD, 
M.A., Ph.D. (late 1851 Exhibition Scholars). Communicated by Sir 
WILLIAM KAMSAY, K.C.B., F.R.S. 99 

V. TJie Atomic Weight of Chlorine: An Attempt to determine the Equivalent of 

Chlorine by Direct Burning with Hydrogen. By HAROLD B. DIXON, M.A., 
F.R.S. (late Fellow of Balliol College, Oxford), Professor of Chemistry, and 
E. C. EDGAR, B.Sc., Dalton Scholar of the University of Manchester . . 169 

a 2 



VI. Researches on Explosives. Part III. By Sir ANDREW NOBLE, Bart., K.C.B., 

F.R.S., F.R.A.S. page 201 

VII. Colours in Metal Glasses, in Metallic Films, and in Metallic Solutions. II. 

By J. C. MAXWELL GARNETT. Communicated by Professor Larmoi; 
Sec.RS. 237 

VIII. On the Intensity and Direction of the Force of Gravity in India. By 
Lieut.-Colonel S. G. BURRARD, H.E., F.R.S. 289 

IX. On the Refractive Index of Gaseous Fluorine. By C. CUTHBERTSON and 

E. B. II. PRIDEAUX, M.A., B.Sc. Communicated by Sir WILLIAM RAMSAY, 
K.C.B., F.R.S 319 

X. Modified Apparatus for the Measurement of Colour and its Application to the 

Determination of the Colour Sensations. By Sir WILLIAJI DE W. ABNEY, 
K.C.B., F.R.S. 333 

XL The Pressure of Explosions. Experiments on Solid and Gaseous Explosives. 
Parts I. and II. By J. E. PETAVEL. Communicated by Professor ARTHUR 
SCHUSTER, F.R.S 357 

XII. Fifth and Sixth Catalogues of the Comparative Brightness of the Stars in 

Continuation of tfiose Printed in the 'Philosophical Transactions of the Royal 
Society' for 1796-99. By Dr. HERSCHEL, LL.D., F.R.S. Prepared for 
Press from the Original MS. Records by Col. J. HERSCHEL, R.E., 
F.R.S. 399 

XIII. On the Accurate Measurement of Ionic Velocities, with Applications to Various 
Ions. By K. B. DENISON, M.Sc., Ph.D., and B. D. STEELE, D.Sc. Com- 
municated by Sir WILLIAM RAMSAY, K. C.B., F.R. S. 449 

XIV. On Mathematical Concepts of the Material World. By A. N. WHITEHEAD, 

Sc.D., F.R.S., Fellow of Trinity College, Cambridge 465 

Index to Volume 527 



LIST OF ILLUSTRATIONS. 

Plates 1 to 13. Sir ANDREW NOBLK : Researches on Explosives. Part III. 

Plates 14 to 20. Lieut. -Colonel S. G. BURRARD on the Intensity and Direction of 
the Force of Gravity in India. 

Plate 21. Mr. J. E. PETAVEL on the Pressure of Explosions. -Experiments on Solid 
and Gaseous Explosives. Parts 1. and 11. 



ADVERTISEMENT. 



THE Committee appointed by the Royal Society to direct the publication of the 
Philosophical Transactions take this opportunity to acquaint the public that it fully 
appears, as well from the Council-books and Journals of the Society as from repeated 
declarations which have been made in several former Transactions, that the printing of 
them was always, from time to time, the single act of the respective Secretaries till 
the Forty- seventh Volume; the Society, as a Body, never interesting themselves any 
further in their publication than by occasionally recommending the revival of them to 
some of their Secretaries, when, from the particular circumstances of their affairs, the 
Transactions luid happened for any length of time to be intermitted. And this seems 
principally to have been done with a view to satisfy the public that their usual 
meetings were then continued, for the improvement of knowledge and benefit of 
mankind : the great ends of their first institution by the Royal Charters, and which 
they have ever since steadily pursued. 

But the Society being of late years greatly enlarged, and their communications more 
numerous, it was thought advisable that a Committee of their members should be 
appointed to reconsider the papers read before them, and select out of them such as 
they should judge most proper for publication in the future Transactions ; which was 
accordingly done upon the 26th of March, 1752. And the grounds of their choice are, 
and will continue to be, the importance and singularity of the subjects, or the 
advantageous manner of treating them ; without pretending to answer for the 
certainty of the facts, or propriety of the reasonings contained in the several papers 
so published, which must still rest on the credit or judgment of their respective 
authors. 

It is likewise necessary on this occasion to remark, that it is an established rule oi 
the Society, to which they will always adhere, never to give their opinion, as a Body, 



upon any subject, either of Nature or Art, that comes before them. And therefore the 
thanks, which are frequently proposed from the Chair, to be given to the authors of 
such papers as are read at their accustomed meetings, or to the persons through whose 
hands they received them, are to be considered in no other light than as a matter of 
civility, in return for the respect shown to the Society by those communications. The 
like also is to be said with regard to the several projects, inventions, and curiosities of 
various kinds, which are often exhibited to the Society ; the authors whereof, or those 
who exhibit them, frequently take the liberty to report, and even to certify in the 
public newspapers, that they have met with the highest applause and approbation. 
And therefore it is hoped that no regard will hereafter be paid to such reports and 
public notices ; which in some instances have been too lightly credited, to the 
dishonour of the Society. 



PHILOSOPHICAL TRANSACTIONS. 



I. On the Normal Series Satisfying Linear Differential Equation*. 

By E. CUNNINGHAM, 13. A., Fellow of St. John's College, Cambridge. 

Communicated by Dr. H. F. BAKER, F.If.S. 

Received December 14, 1904, Read December 15, 1904. 



CONTENTS. 

Section Page 

1. Introductory ........ . .................. 1 

2. The equations to be considered .and the canonical form of a linear system of equations . . 3 

3. The solution in view ........................ 4 

4. The unique determination of the determining matrix when the roots of the characteristic 

equation are unequal ....................... 5 

5. The completion of the solution in the same case ............... 

6. The general case; restriction on systems considered .............. 10 

7. The matrix x ; preliminary assumptions as to its form ............. 11 

8. The difference equations for the coefficients ; equations of condition ......... 11 

9. On certain operators A r and their application ......... ....... 14 

10. The particular case when the roots of a certain equation are unequal ........ 16 

11. The non-diagonal elements of x in this case ................. 19 

12. The complete solution for p 1 in this case ................. 21 

13. The solution forp = 1 in the general case ................ 

14. Resumption of most general form .................... 25 

15. Application of the method to a particular equation .............. 29 

16. On the method to be adopted when certain equations of condition are not satisfied; sub- 

normal forms ......................... 30 

17. Complete solution of a certain equation of the third order ............ 34 

1. THE present paper is suggested by that of Dr. H. F. BAKER in the 'Proceedings 
of the London Mathematical Society/ vol. xxxv., p. 333, "On the Integration of 
Linear Differential Equations." In that paper a linear ordinary differential equation 
of order n is considered as derived from a system of n linear simultaneous differential 
equations 



or, in abbreviated notation, 

dx/dt ux, 

VOL. CCV. A 387. B 21.6.05 



2 MR. R CUNNINGHAM ON THE NORMAL SERIES 

where u is a square matrix of n rows and columns whose elements are functions 
of t, and x denotes a column of n independent variables. 

A symbolic solution of this system is there given and denoted by the symbol fl(u). 
This is a matrix of n rows and columns formed from u as follows : Q(<) is the matrix 
of which each element is the (-integral from t to t of the corresponding element of <, 
(j) being any matrix of n rows and columns ; then 

wQw...ad inf., 



where the operator Q affects the whole of the part following it in any term. 
Each column of this matrix n(n) gives a set of solutions of the equations 

dx/dt = ux, 

and since fl(n) = 1 for t = t , these n sets are linearly independent, so that fl(u) may 
be considered as a complete solution of the system. 

Part II. of the same paper discusses the form of the matrix Sl(u) in the neighbour- 
hood of a point at which the elements of the matrix u have poles of the first order, 
or in the neighbourhood of which the integrals of the original equation are all 
" regular." 

It is there shown that if t = be such a point, a matrix 



0* c,. 2 (t/t ) e - 

0. 



can be found, in which all elements to the left of the diagonal are zero, in which 
c^ = unless t Q } is zero or a positive integer, such that fl(u) is of the form 



where G is a matrix whose elements are converging power series in t, and G is the 
value of G at t = t a . 

The form of <f> is such as to put in evidence what are known as HAMBURGER'S sub- 
groups of integrals associated with the fundamental equation of the singularity ; the 
method is, in fact, a means of analysing the matrix fl (?t) into a product of matrices, 
of which one is expressible in finite terms and shows the nature of the point as a 
singularity of the solution. 

The object of the following investigation is to see how far, under what conditions, 
and in what form, such an analysis can be effected for equations having poles of a 
higher order than unity in the elements of the matrix u. 

It is known that if in the neighbourhood of infinity the equation is of the form 



X 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 3 

p r being a polynomial of degree pr, and P r (l/.x) a series of positive integral powers 
of l/x, the equation has a set of formal solutions of the form 



r = 



where il r is a polynomial of degree p+\, provided a certain determinantal equation 
has its roots all different. 

The case in which these roots are not all different is discussed by FABRY (' These, 
Facultd des Sciences, Paris,' 1885), where he introduces the so-called Subnormal 
Integrals, viz., integrals of the above form in a variable x r ' k , k being a positive integer. 

The investigation carried out in the following bears the same relation to the 
discussion of these normal and subnormal integrals that Part II. of the paper quoted 
at the outset bears to the ordinary analysis of the integrals of an equation in the 
neighbourhood of a point near which all the integrals are regular. 

2. Throughout the discussion the neighbourhood of the point t = will be under 
consideration, the coefficient p r being supposed to have a pole of order ts r at this 
point. 

Let p+l be the least integer not less than the greatest of the quantities rav/r. 
The equation may then be considered as belonging to the more general type 



_ A 



where P r (0 is holomorphic near t = 0. 

This equation may be reduced to a linear system of simultaneous equations as 
follows (vide ' Proc. Lond. Math. Soc.,' vol. xxxv., p. 344) : 

Put x, = z, o- 2 = ^ +1 z (1> , ... sr r+1 = t r(f+1 W r \ r=l,..,,n-l. 

The n equations then satisfy the system of n equations 







(n-5 



dx 


' l 


dt 


t pv 




o p+l l o 




1 1 


i 


o, 




Qi 




t p+l ' 



where Qi...Q n are series of positive integral powers of t. This system belongs to the 
more general form 

B 2 



ME. E. CUNNINGHAM ON THE NORMAL SERIES 






where a p+1 ...ft... are square matrices of constants. 

The most general equation of this form will be considered. 

If p. be any matrix of constants and y = px, the n quantities y satisfy the system 



a 
or 



Let /i be now chosen so that (p^fT 1 ) is of canonical form as follows :- (i.) It has 
zero everywhere save in the diagonal and the n-1 places immediately to the right of 
it ; (ii.) The diagonal consists of the roots of the equation a p+l -p\= 0, equal roots 
occupying consecutive places; (iii.) The elements to the right of the diagonal consist 
of (e,-l) unities, then a zero, (e 3 -l) unities, a zero, and so on (' Proc. Lond. Math. 
Soc.,' vol. xxxv., p. 352). 

Form now the matrices (/lo^' 1 ) ...(/tftfT 1 ) ; the equation is then replaced by an 
equation of exactly similar form, the matrices a,,... being still any matrices whatever, 
but Oj, +1 being of the canonical form. 

3. The equation being denoted by 

dy/dt = uy, 

if 77 be any solution of the equation 

(A) drjjdt = U7)-r)x, 

X being an arbitrary matrix, we have 



so that i/n (x) is a matrix satisfying the equation in question. 

In what follows we are concerned with the form of a solution more than the actual 
convergence and existence of the same. It is therefore important to notice that if 77 
be a diverging power series formally satisfying equation (A), 770 (\) may be still 
considered as a formal solution of the original equation, the only condition necessary 
to secure its actual existence being the convergence of 77. 

If 77 be convergent, the solution may be particularized by adding the factor ij ~ l t 
i.e., 170 (x)^)" 1 i s the solution reducing to unity at t = t a . 

The main investigation to be carried out is that of a simple form for the matrix x, 
such that the subsidiary equation (A) may have a formal solution in the form of a 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 5 

matrix whose elements are series of positive integral powers of t, reducing for t = 
to the matrix unity. 

4. Owing to the much greater simplicity of the case in which the equation 
\a p+l p\ = has all its roots different, it will be treated first separately. The result 
obtained is as follows : 

A matrix x can be determined uniquely of the form 

Xi+i i XP i i Xi 

tn+ 1 ' j i * * i , ) 



where XT>+I ---Xi are Matrices of constants in whicli all elements save those in (he 
diagonal are zero, such that there is a formal solution 



where the matrix rj is made up of series of positive integral powers of f generally 
diverging and reducing for / = to the matrix unity. 
Consider the equation 

(B) $- - 

where 

r = I.,..., p+\. 




The roots of ot p+l p\ = being unequal, the matrix y)+1 will have zero elements 
except in the diagonal; the diagonal elements will be /3 1; p.,, .../>, the roots of the 
equation. 

If the equation (B) is satisfied by the matrix 

i) = (x, y, z...}, 
where x, y, z ... denote columns of elements of the form 



X = X 

y = y+yit+..., 

the coefficients x r , y r ... being columns of constants x r a , x r \ x r 2 , &c., these constants 
satisfy the following equations : 

X. (a p+l 6 1 p ^ l )x = 0, 

a +1 -0nz, + -<V)* = 0, 



MR. E. CUNNINGHAM ON THE NORMAL SERIES 

+ i*+- +( 1 -0 1 1 )* = 0, 



A precisely similar set of equations gives the relations connecting the constants 



The equations X just written determine uniquely a set of values for l p+l ...0 l l and 
the coefficients .r .... 

The first of these equations gives 



m 

Since r,, is to be equal to : \ve must have 6\, +1 = /3 1( and these equations are 

\0/ 
then satisfied. , , 

Similarly the first of the ?/ equations with ?/ = gives 2 p+} = p 2 ; and so for 

W 
the other columns. 

The second of the equations X written more fully gives 

<'-0; = 0, (p r -pi)*, r + V r = 0, * = 2 . > w. 

These then determine x l save for its first element, in place of which a unique value 
is given for p l . 

The third equation X in full gives 



x 1 " + a 1 V 1 = 0, r = (2, ..., n). 

Of these, the first gives l f -i, while the following determine sc 2 save for its first 
element, but only in terms of the yet undetermined .r, 1 . 
Of the next group, the first equation is 



This equation apparently involves the unknown .r, 1 explicitly, and also, in x 2 2 ...x 2 ", 
implicitly. 

But the whole coefficient of x r l is 

U 



pS-p,/ 2 

'i n 

2 2 ' 

EO that ^-2 is given independently of o^ 1 . 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 7 

The remaining equations of this group give x 3 except for x 3 \ in terms of x^ and x, 1 . 

Proceeding in this way as far as the (p+l) th equation of X, x^...x p are all found 
except for their first elements, while the first elements of these equations give 
6 l pJrl ...0i, l p+r being not a priori independent of x^...x r l hitherto unknown. 

It has been shown above, however, that the determination of 6 l p ^ 1 does not require 
a knowledge of x. 

In general, in fact, () l p - r is given independently of x^.-.x, 1 . 

To prove this, the way in which x^ enters into .x-* r+1 will be first considered. This 
may be stated .as follows : 

The coefficient of x in x\ +l is equal to that part of x r k which is independent of 

For r = 1 this is at once seen by writing down the equations 



In general the equation for .r A r+1 is 



Assuming the statement above to be true for 1, 2...r, and that 9 V , ..., p - r+ i are 
independent of x 1 l ...x l r - l , the above equation shows that the coefficient of x^ in 
(pt pi)x k r + l is the part independent of a?! 1 ,..., ,r r l in 



r I 

, V /-,!* .''j- - r, 

li i \ a p-r-n+l^j T...-rt* p _ r+< + iX s j-, 



i.e., u 



so that under the above assumptions the statement holds for 1, 2..., r+1. 
Also, under the same assumptions, from the equation giving l ; ,- r , viz., 



we deduce that the coefficient of x/ in ^p-,. is the part independent of x^ in 



This expression differs only from the left-hand member of the equation for 6 l p - r+ i 
by multiples of x^^.x 1 ^^ and therefore, on the assumption that this equation gives 
^P-! independently of a?/..., the part independent of these quantities in the above 
expression must, when 6 l p - r +i is determined, vanish, so that 6 l p - r is independent of x, 1 . 



8 MR. E. CUNNINGHAM ON THE NORMAL SERIES 

Now the way in which the successive equations follow one another shows that the 
coefficient of aV in 6* is equal to that of a:, 1 in ft+r _,. 

Thus 0',,-r+i being independent of a^ 1 , l p - r is independent of x 2 \ and in general, 
l p -,+ k (k = l...r-l) being all independent of a^ 1 , Q l p - r does riot contain x^..^,^. 

Thus, if the assumptions made on p. 7 are satisfied for any particular value of r 
less than p, they are satisfied for a value of ? one greater than that value. 

For ? = 1 the statements have been justified, and it follows therefore that fl 1 ^...^ 1 
are all determined uniquely without the knowledge of a;, 1 , x 2 \... from the first (p+l) 
of the equations X, and by the same equations x^-.x^ are found, except for their first 
elements, the expressions obtained containing those first elements. 

5. Consider now the (p + 2) Ul equation X in regard to its first element. 

As before, this will be independent of x p l ...x 3 l ; but on account of the extra term 
arising from dy/dt, which now enters for the first time, the coefficient of aV is not 
zero. 'It is, in fact, 1. 

Thus, the quantities 6 l l ...6 l p+l being now known, this equation gives a^ 1 . 

Similarly, the next group's first member will contain the term ZxJ but will not 
contain x-}.,,x l p + lt and will therefore give x 2 l after o^ 1 is found. 

Thus all the elements x^ are determined successively, and returning to the 
expressions for a?/ (?'>l) in terms of these and substituting the values so found, all 
these are given also. 

The equations for the columns y, z, &c., being treated in the same way, give the 
corresponding O's uniquely, and also the coefficients in the series of which these 
columns are composed. 

Thus it is shown that when the "characteristic equation" p+ i p\=0 has its 
roots all different, the equation 

dy/dt = ny, 
where 



a p+ i being in its canonical form, possesses a unique formal solution in the form 



where the elements of Xp -- Xi llot "i the diagonal are zero, and the elements of r? are 
power series in t, reducing for t = to the matrix unity. 

The matrix n^ + ... + j can at once be written in the form a>/a> , where o> is 
a matrix whose non-diagonal elements are zero, and whose k ih diagonal element is 



e p- tr 
and w is the value of CD at t t lt . 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 9 

If the series t) happen to be convergent, the solution which reduces to unity at 
t = t can at once be written in the form i)<ato ~ 1 r} ~ 1 . 

Applied to the system formed from a particular linear ordinary equation we have 
at once the result referred to on p. 3 (v. SCHLESINGER, ' Lin. Diff.-Gleichungen,' 
vol. I, pp. 341 ff.*). 

As a simple example of the application of the method we may take the well-known equation 
Putting Wi = w and W-T, = s 2 dw/dt 



dz* 



. w. 



which in matrix notation is 



The equation p 

a. -p 



to canonical form is 



du/dt = 



= VM, say. 
The subsidiary equations are 



t = - - + + y w l + w,, 

\Z Z j Z 



w. 



= gives p = \/a, and the matrix //, needed to transform the first matrix 



, so that the equation is transformed to 



i 



+ JL I___N 



which give as the general relations connecting the coefficients of the first column of ?;, putting i> = 1 + -J A, 

(i.)- 



- Tia^, 1 + ^ 2 + j-Zj- (a; 1 ,,.! - x 2 ,,,!) = 



- 2 



-> - m 



^-^ (^,.-1 - 2 -i) = I 



- 2 



Hence 

and therefore 

- 

which with the first equation gives 

2 V . n (x 

Thus a recurrence formula is established for the quantities x n l -x n 2 in terms of which a; 1 ,^! and a; 2 ,,+i 
can be at once expressed. 

* With reference to SCHLESINGER'S demonstration of this result, see a note by the author in the 
'Messenger of Mathematics," January, 1905. 

VOL. CCV. A. C 



10 MB. E. CUNNINGHAM ON THE NORMAL SERIES 

The series for x will terminate if for any value of n 

y + (q-n)(p + n-l) = 0, 
? f if 



for some value of n. 

The series for y will similarly terminate if 

(-A + 2/-l) 2 -(4y + l) 
vanish for some value of n. 

Both these are certainly satisfied if 

X = q and 4y + 1 = p 2 , 
where p, q are any integers of which one is odd and the other even. 

6. We pass now to the case where the characteristic equation \a p + 1 -p\ = has its 
roots not all unequal, and the analysis becomes a good deal more intricate with the 
less simple canonical form of the matrix a p+1 as stated on p. 4. It will be remembered 
that the numbers e 1; e 2 ... there used are the powers of (p^-p) in the elementary 
divisors of | a p+1 -p \ with respect to the root p l of this equation of multiplicity I In 
the case of the system obtained on p. 4 from a single equation of order n, we may 
prove that ^ = I, e 2 = e 3 = . . . = 0. 

For the matrix (a p+1 p) is of the form 



/ 


i 




. 

1 . 


. . 


\: 


b 





. 1 

. . k 




The minor of the quantity " k" in the determinant of this matrix is simply 
( p}"~\ Thus the elementary divisors are certainly merely unity with respect to any 
non-zero roots. 

If there be a multiple zero root, however, since the minor of "a" is unity, the 
elementary divisors with respect to this root are all simply p u . 

Thus for such a system we have for each multiple root e 3 = e 3 . . . = ; so that in the 
canonical form of a p+1 , if 

Pi = pi+i> a p+i' ' = 1 
and if 



Such systems being by far the most important in practice and also considerably 
simpler to work out, the full discussion will be restricted to systems of this type. It 
may be pointed out that the most general system can be solved by means of the 
solution of systems of this more restricted type, for from the general system 



SATISFYING LINEAE DIFFERENTIAL EQUATIONS. 11 

ft *T' tt 

-T- = jj+i %, where u is a power series in t, a linear equation of order n and rank p 

near t = can be obtained for each row of the matrix x, and this equation can be 
solved by the solution of a linear system of the restricted type in question. 

Of the matrix ^ to be used here, the following properties will be presupposed : 



(i.) It is to be of the form % + % + ...+& } where each of the matrices 

V V V 

XI---XP+I has all elements to the left of the diagonal zero. 
(ii.) The diagonal elements of these matrices are to be numerical constants 

denoted as before by r * (r = 1, ... , p+ 1 ; s = 1, ... , n). 
(iii.) All the other non-zero elements of x^Xs-'-Xp-t-i are t be constants, while 

the other elements of ^i may contain t, but only to positive integral 

powers (cf. the matrix x in Dr. BAKEE'S paper, loc. cit.). 

8. As before, the matrix 77, which is a formal solution of the subsidiary equation 

drjjdt = UTf)r)x, 
will be supposed to be formed of the columns 



y = 2/0 

and the equations for the coefficients x r y r ... are the same as the equations X (p. 5). 

But the detailed form of these equations is quite different. The first of them 
( ,,+! l p +i)x = is still satisfied by 

3. | I #' n 

~ y i ' ^ p+i ~ PI- 

Supposing now p, to be a root of multiplicity e l} the second equation X is in full 



= = 
= 0, 



where 

p f ,+i = = p t ^,,^ 

C 2 



12 MR. E. CUNNINGHAM ON THE NORMAL SERIES 

These equations manifestly determine x^ except for its first and second elements, 
the second being known as soon as p l is. 

We are also at once faced with a condition necessary for the possibility of the 
solution under the assumptions made as to the form of x, viz. : 

/' = 0. 

This condition arises from the e," 1 equation of the set, and as, in the ensuing 
discussion, the e^' 1 equation of each set is most important we shall here introduce a 
notation for it, viz., X r will stand for the e/ 11 equation of the (7-+l) th set; i.e., of the 

set 

(a f + l -0 l p + l )x r +... = 0. 

This equation will not contain any element of x r . 

A similar notation will be adopted for the equations Y, Z... for the coefficients in 
the other columns of TJ. 

If the second element of the first row of X P +\ t e C 2\, the equations Y are 

(^-H-tf'W l)2/0-^0 = 0, 

(a.j,+i-8 a 1 ,+i)yi+(a. f -0 p )y -c lsl x 1 = 0, 



Of these the first is satisfied by 




provided we take c 21 = 1 = corresponding element in a p+l . 

Considering each of the columns in succession we have thus, with i) = 1. 
XP+I = a p+\- 

The second of the equations Y gives 

-X 1 1 = 0, 

-V-xf = o, 



atp 8 "'- fl^* = 0, 

(j^i-/'i)2/ 1 ei+1 + <' +1 -*i ei+1 = 0, 

which, when x l is known, determine y l save for its first element, and its third until 
OP is known. 

The exceptional equation Y,, af'-xS = 0, gives us again a necessary condition for 
the possibility of the solution in view, a/^' + a'- 1 = 0, 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 13 

Similarly the equation Z l gives 

= a/' "-y,'' = /" + < "-'-a^'- 1 = a/^' + a/'''-'*^'.'.- 3 , 

and so on for the equations for each of the first e t columns of r). 

For the (ej + l)" 1 column, however, the non-diagonal term of x*+i = and the 
equations for this column do not contain the elements of the preceding column. 

In fact, the e 2 columns beginning with the (cj + l)" 1 form a group related to one 
another in just the same manner as the first e x are. We obtain from them, as from 
the latter, the conditions 

, + !,<! + t, A 

a. p \J, 



and so for the columns associated with each group of equal roots. These and other 
conditions which arise in the course of the investigation will be called " equations of 
condition." Supposing those already found to be satisfied, we may return to the 
solution of the equations X, and of these the following statements are to be 
proved : 

I. The first e[ 1 equations of the (r+l) th set determine x r 2 ...x r f < in terms of 
^...aj 1 ,-! and l p+l ...0 l p - r+1 ; the equations from the (ej+l)" 1 onwards give .r/ 1+I ....r r " 
in terms of the same quantities. 

II. When the values thus found are substituted in the equation X r+1 , the resulting 
left-hand member is independent of the undetermined quantities .r, 1 ...^ 1 , B p l ...0\- r for 
all values of r up to (e 2 2), but for r = Ci 1 it is independent of all save B p l ; in fact, 
the equation X ei is an algebraic equation of degree e t for p l and contains no other 
undetermined quantity. 

III. Supposing one root of this to be chosen for the value of B p , and the equations Y 
to be treated in the same way, Y ei _j will be an equation of degree (e l 1) in B p 2 , 
whose roots are exactly the remaining roots of X v 

IV. Similarly Z E| _ 2 furnishes an equation of degree EI 2 for B p \ whose roots are the 
remaining roots of Y,^, and therefore of X i , and so on. 

Thus B p l ...B p ' are the roots of the equation X ei . 

V. The values of #,,_!... subsequently obtained in association with each of these 
roots will be the same in whatever order they are taken. 

Of these I. does not require proof. 

With regard to II., the proof that the equations do not contain the undetermined 
a;'s follows exactly the same lines as the corresponding proof when the characteristic 
equation has its roots all diiferent (vide pp. 7-8). 

The proof that they do not contain 6 P . . . until r = ej 1 requires considerations of a 
different kind involving the equations X, Y, Z... simultaneously. 



14 MR. E. CUNNINGHAM ON THE NOEMAL SERIES 

9. Consider the system of equations X 1 derived from X by changing 6J into 6 f > 
and x into x 1 , viz. : 

X 1 . K+i-^VOxo 1 = 0, 



and let these be treated in exactly the same way as the equations X, the undetermined 
elements of x 1 being supposed the same as those of x. 

From the two sets of equations X, X 1 let a new set be formed by subtracting 
corresponding members of X and X 1 and dividing each remainder by P -0 P 2 , and let 

this new system be denoted by 

X-X 1 _ Q 

The expressions for x 1 obtained from X 1 in terms of 1 p + l ... will be identical with 
those obtained from X in terms of the same with p l changed into P ". 

xx l 
Let A P .T denote the expression ' ' 

Vp Up 

Then A ;) X is the system of equations 

= 0, (+, - 0Vi) A/d ~X = 0, 

a 1 /9* ^A / y-l-//v $ \ \ T:-. T,-, = 

\ w+l " p + 1 / *-*/>'^'2 ' \ p u p I *-*p'* J l * JU \ v ? 



Further A p (;r 1 ) = [ M = y 0> and l p+1 = 



Thus these equations are identical in form with the equations Y, except that 2 p - k 
is replaced by 6 l p - k , &>0. Thus if from Y the y's be calculated as in I., p. 13, and 
from A P X the quantities \x be similarly determined, the only difference between 
Aa? r+1 and y r will be in the substitution of x... for t/i 1 ... and 6 l p - k for 2 p - k , A;>0, and 



Thus if we substitute the values of A p a; thus found in ApX^! the result will differ 
from Y r only by the same substitutions. 

In a similar way, denoting by A P Y the difference equations 

Y-Y 1 



P *-0 P 3 



A P Y will differ from Z r _j only by the substitution of y?... for z?, tf v - v for 0^..., and 
0*+l for 0J 3 , and so for the remainder of the first e l columns. 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 15 

In exactly the same way if X 2 denote the system derived from X by the change of 
p _! into &p-i, and the equations 

Y X-X 2 

p- 1 ^ ~" ai on 



be formed, the quantities A,,_ 1 a.v+2 differ from y r only by the substitution of 6 p for 9 P \ 
l p - 2 for 2 p - 2 ... and 6^ + 2 for 6*. The same operator A p _j applied to the equations Y 
connects the columns y and z, and so on. 

Similarly, operators A p _ 3 ...A a may be defined. 



X 

Lastly, an operator Aj may be defined so that the equation AxX is -^-r where 

"i PI +p 



denotes the equations X with O-fp substituted for 8*. Then the equation Y r 
will, when y^,... are replaced by aV,... and B p 2 ,..., 2 2 by P 1 ,..., 2 l , become the 
equation A ? X p+r . 

Consider now the equation Z l ; it is independent of #/, Zi 1 ,..., and therefore reduces 
to a simple numerical constant which must be zero (p. 13). 

But Y is a polynomial in 6*. It can therefore be only of the first degree, since 
A P Y 2 is independent of P 3 ; is, in fact, the same as Z,, viz., zero, so that Y 2 does not 
contain P 2 . It must then, like Z,, be only a constant, and must therefore vanish 
identically, so that Y 2 = gives a further " equation of condition." 

Hence again X 3 cannot contain p l , and the operator A p _! connecting it with Y, 
shows that it cannot contain l p -i. Thus X 3 again must be a vanishing constant, 
giving another "equation of condition." 

Similarly, starting with the corresponding equation of the fourth column, we 
find A P X 4 = 0, so that X 4 must be independent of 6 P . Also A^X, will vanish 
identically, so that X 4 is independent of 6 l p - 1 , and similarly it is independent of 
ffi p . a .... 

Thus if ej > 4, X 4 reduces to a mere constant which, as before, must vanish. 

The process may clearly be carried on as far as the e^' 1 column, so that the equations 
Xi.-.X,^! all give equations of condition, as do also Y^.-Y^-js, Zj.-.Z^-a, etc. Starting 
now from the second equation of the e/' 1 column, 



where ^ denotes the e^ column of TJ, it follows that the third equation from (e^ l) th 
column must be a quadratic in 9 p -^~ l , independent of & 1 , {= <f> 2 (0p'~ l ) say}, and 
such that 



Thus if 0/ 1 " 1 is one root of </> 2 = 0, 0/' is the other. 



16 MR E. CUNNINGHAM ON THE NORMAL SERIES 

Similarly, the fourth equation from the preceding column must give a cubic for 
e p '~\ (fo = 0), such that 



Thus 0/'~ 2 , 0/ 1 " 1 , p tl are the roots of < 3 = 0. 

Eventually the first column gives an equation of degree e t for P (viz., X ei ), of which 
the roots in any order are a possible set of values for p l ...0 p f '. Calling this equation 
(f> (6} = 0, and denoting its roots in some assigned order by <r lt cr 2 , ...cr ] , let us consider 
the values determined for l p -i... by taking p l = ov.. and P '' = <r tl . 

10. Again, as prior in order of simplicity, let the case in which the roots of <j>(0) 
are all different be taken first. 

It has been shown above that the equation Y r , when x^... are substituted for y?... 
and P \ 6 l p - 2 ... for P 2 , 2 p - 2 ..., becomes identical with A p _iX r+2 . 

Now, Y I _! is merely a polynomial in 6 P , independent of?/! 1 ... and 2 P - 1 ..., and 
vanishing for P 2 = cr 2 , o- 3 ...cr ei . 

Let Y.,., = *_,(*/). 

Thus X ei+1 is linear in 6 l p ^ the coefficient of the same being ^,^(0^); the part 
independent of 6 l p ^ contains only P , which is now a determinate quantity. 

If the roots of <j) ei (0 p ) are all unequal, ^.^^^O and 6 l p -^ is given uniquely ; and 
similarly Y t] = is a linear equation for 2 p _i in terms of P 2 and 6 P , Z ] _! a linear 
equation in 3 p -i, and so on. 

It is important now to consider whether the order in which the roots o- 1 ...o" ei are 
taken is of significance in the solution ; that is, whether the value of ff'p-i associated 
with a particular root a- k is the same whichever column of the dependent variables 
this root is associated with, and whether a change in the order necessarily implies a 
distinct solution, because, if so, the solution would appear to be by no means unique. 

The equation X, i+1 giving l p ^ is, we have seen, of the form <^ 1 (o- 1 )^ 1 p _i + />(o"i) = 0, 

where #(8) = 
Thus 



Now fifa) is save for a constant factor 

(0-1-0-2) (o-j-o-a)...^-^), 
so that ApX i+1 is 

= 0. 



But the equation Y I , which is independent of 0*,_,,... becomes, when p l (= a-,) is 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 17, 

substituted for P ', the equation A p _ 1 X, i+2 , so that when 6* is substituted for 6 a 'n\ 
Y t| it becomes symmetrical in 6 l p ^ and a p -i. Y I must therefore be of the form 

A(<r lf ir,)tf l r . 1 +B(a I ,<r 1 )V.i+0(<r to ir i ) - 0, 
where 

A(o-i, o-j) = B(o-i, o-j) 
and 

A(<TI, o- 2 ) + B(o-,, o- 2 ) = (o-j-o-g)... +(0-3-0-.,).... 
Hence 

A{o-!, o-j) = (o-i 0-3) (o-i 0-4)... = B(cri, o-,). 

Now before the values of #/, #/ are substituted in Y I the coefficient of 6 2 P ^ must 
be a function of p a only. 

Therefore B must be a function of o- 2 independent of cr,. 

Hence 

B = (cr,-o- :i )...(o-,-o- ti ) 
and 

A = (cTi 0-3)... (o-j 0- t| ). 

The equation for $ 2 p _i is therefore 



By virtue of the equation giving #^-1, therefore, we have 

(o- 2 -o- 3 ). ..(o 2 -o %i )6V 1 + ^-- = 

tr a o"! 

as the equation for ^_!. 

But this is identically the equation that would have been obtained for l p -i if 
0-,, o- 2 had been interchanged. Thus the value of 6 P -^ associated with the root cr., is 
unaltered by this interchange. 

We have further to see that the same permutation does not alter the 6 p ^ l for the 
subsequent columns. 

In just the same way as above the equation for 6 3 p -i is shown to be 



( W } O 2 + ' } 6 S + ' 2 ~ g ' 1 (r 3~ Cr l _ Q 

which gives 



independently of the order of o-j and o- 2 . 

The same holds for 6 k p -i, k < c^ and a similar proof for the interchange of any other 
pair of the roots o-. 

Thus supposing the roots of <f> (6 P ) = to be all different, there is associated with 
each a unique determinate value of f -i. 

VOL. CCV, A, D 



lg MR. E. CUNNINGHAM ON THE NORMAL SERIES 

These quantities then being determined, consider now the equation X ,+ 3 , Y, 1+1 ... 
and first it must be pointed out that the relations established between the equations 
X Y... through the operators A (pp. 14-15), where the quantities 6 P , 0^... were 
considered as independent, are still valid when P ^, &c., are determined as functions 

of 6 

The operator A, in the first place becomes replaced in the equation X, i+2 after that 

giving 0',-! b J ^ + Vi--VF?F- But ViX., vanishes owing to the choice of 

"p Up 

0Vi. so that the value of 6\^ being substituted in X e , +2 the operator A p may be still 
applied to establish a relation with Y, I+ I. 
We have further 

VA. = &-i(V). 

while A p _ 3 X,, +2 ... vanish identically because of the vanishing of Y,,- 2 , Y ei _,.... 
Thus the equation X, i+2 is of the form 



in which p l and 1 p - l are to have their determined values, so that the equation may 
be written 



The operation A p having been shown to be applicable to the equation in this form, 
reasoning exactly as above shows that the equation for 2 P _ 2 reduces to 



so that the values of (J p - 2 associated with the roots o- 1; cr 2 are independent of the order 
in which these roots are taken, and likewise the values of 6* p -. 2 ... will be unaltered 
by a permutation of the same. The same may be shown in the same way of a 
permutation of any other two consecutive roots, viz., that such permutation gives rise 
to a corresponding permutation of the 0^_ 2 .... Identical reasoning leads to an 
identical conclusion with regard to Q p -. a ...0 2 . 

Eventually we come to equations giving #,. When d p l ...0 2 l have all been found, 
the equation 'K fi+p . l is of the form ^-i^ij^+x^i) = 0, where, as before, the 
coefficient of 6* is not zero, so that 6* is determined like the rest ; while l 2 ...0i 1 are 
found respectively from Y ei+p _ 2 .... 

All the 6's being now determined, if we pass to the equation X, 1+p and follow the 
same argument that was required to prove the preceding equations independent of 
Xj 1 ..., the coefficient of x is found to be the left-hand member of X. 1+p _i with (^ + 1) 
substituted for 0^, i.e., it is simply $,^(0-1), which is not zero. Thus X. 1+p determines 
the first of the undetermined elements x ____ 

Similarly in X, 1+p+1 the coefficient of x 2 l is 2< Ci _ 1 (o-i), so that by this x a l is given, 
and so on for the succeeding equations in turn. 



SATISFYING LINEAR DIFFERENTIA!, EQUATIONS. 19 

In order to proceed to the determination of the second column it may be noticed at 
once that the coefficient of y r l in any equation is exactly equal to that of x r l in the 
corresponding equation from the first column with o-j and cr 2 interchanged, which 
includes the interchange of l p - k and 6 2 p - k . In the equation 'Y, i+p _ l , therefore, the 
coefficient of y^ is identically zero, while the unknown 6-Js are now all determined. 
The closer consideration of this equation is deferred for a moment. 

The coefficient of y in Y, i+p = coefficient of x* in X, i+p with o^ and <r 2 interchanged 

= (<r a <7i)(er a o- 8 )...(crg o-.,) i= 0. 

Similarly the coefficient of y% in Y n+p+1 , and in general of y k l in Y + p + k _-i, is not 
zero, while Y ei+p+i _! does not contain any element y m * for which m>k. 

For the third column the equation Z ei+p _ 3 determines 0^, and the two equations 
following, Z, i+p _ 2 , Z. i+ p_!, are still independent of z^, z 2 1 ..., while the equation 
Z.j+p+A-! contains z^...z^, the coefficient of z k being &(cr 3 o-i)(o- 3 cr 2 )(cr 3 o-.,) 

In the same way, if the elements of the e t ih column be denoted by and the 
associated equations by ft, the equation l p determines 0^', ft ;j+ i...ft ;)+6i _ 1 do not contain 
fi 1 ..., and ft,+,, contains & 1 only. 

11. So far the matrices XP---XI nave been taken to be simply diagonals. It will now 
be shown that the insertion of constants to the right of the diagonal in the first e v 
columns of XP can be carried out in such a manner as to affect none of the conclusions 
hitherto made, while they may be chosen so that the equations Y^^, Z, i+p _ 2 , 
Z.^p-j, &c., are all satisfied. 

Denoting by a,-,- a constant in the i ih column and _/ th row, i>y, i^f\, ,/<fi, the 
Y equations become 

(0) (a ?)+1 -^ 41 )7/ -.r,,=0. 

(1) (a p+1 ~0 p ^)y l + (a p -0 p )y a -x l -a !>l x =0, 



(r+l) (a p+l -0 p+l )^ r+1 + (a p -0 p )>/ r ...-.r r+l -a.-\r r = 0. 

These equations are to be treated just as they were before the constants a were 
introduced the same elements remain undetermined as before, but at each stage the 
quantities found presumably contain a 21 . 

We see at once from equation (1) that the coefficient of 21 in y^ (the first element 
being excepted) is simply y . In fact, it can be shown step by step that the coefficient 
of a 21 in y r+l (the first element always excepted) is exactly that part of y r which is 
independent of a zl with 0^ increased by 1 ; and therefore the coefficient of a 21 in Y r+1 , 
when the values ofy r 2 ... as far as they are known are substituted, is equal to that 
part of the left-hand member of Y r which is independent of a 21 , #/ being increased by 
unity. 

Now Y! is independent of a 21 and of 0^ and vanishes, thus Y 2 is independent of a 21 , 

D 2 



20 MR. E. CUNNINGHAM ON THE NORMAL SERIES 

and is therefore the same as if a 21 were zero. It is also independent of ft, 2 , so that Y 3 
again is independent of a 21 . 

Thus until k is so large that Y* does not vanish independently of 0?, Y i+1 is 
independent of a 21 , and therefore the same as was obtained in the foregoing, where a 21 

was neglected. 

Thus the insertion of a 21 in XP does not affect any of the equations Y^-.Y.^-* and 
therefore the values of P 2 ...6* are independent of a 21 . 

But in the equation Y ei+7 ,_! the coefficient of <x 21 is the left-hand member of Y, 1+P _ 2 

with 0*+l for 6i* 

= (o- 2 -o- 3 )(cr 2 or 4 )... ^ 0. 

Thus a 21 can certainly be chosen so that the equation Y ei + p _! is satisfied. 

Having determined a 21 , it is at once seen from p. 19 that the following equations 
now determine yS, yj... without ambiguity ; for since 0*...$? are independent of a 21 , 
the coefficients of y,\ &c., are those found there whether a 21 be zero or not. 

In the same way for the third column, with a 32 , a 31 , taken into account, the equations 
become 



= 0, 



and just as before the first equation in which : < 2 occurs with a non- vanishing coefficient 
is the one following the equation from which -0* first does not vanish out identically, 
viz., Z ti+;) _ 2 ; while 31 will occur first in the equation homologous to the Y equation 
in which 21 first occurred, viz., Z, i+p _i ; in fact, in Z e|+p _ 2 , a 32 will occur multiplied by 
the left-hand member of Z ei+p _ 3 with 0^+1 put for 0f, and in Z ei+p _ 2 , 31 will be 
multiplied by the left-hand member of Y ei+p _ 2 with 0^+1 put for 0* : both these 
factors are other than zero. 

Thus a :!2 can be chosen to satisfy Z ej4p _ 3 , and subsequently a 31 to satisfy Z, i+p _ 2! 
while the preceding equations are quite independent of them both ; just as for y, then, 
Zf 1 ... are given in succession without ambiguity. 

Treating the remainder of the first Ci columns in just the same way, all the elements 
of these columns are found in succession, and the solution is complete as far as these 
columns are concerned. 

The t- 2 columns associated with the next group of equal roots may be treated in 
the same way, the singular equations being in this case the (e! + e 2 ) th of each set; 
constants a ij will again be chosen in the matrix x to the right of the diagonal, 
Ci + e 3 >: i> i + l, e l + e 2 >j>f l +l, to satisfy certain equations as above, and so for 
each root in succession. 

Thus if the various equations for O p associated with the different groups of equal 
roots of the characteristic equation have their roots all different, and the " equations 



SATISFYING LINEAll DIFFERENTIAL EQUATIONS. 21 

of condition " (p. 15) for each root are satisfied, a formal solution of the linear system 
has been found in the form 

nti(^+Xz+ +Xi\ 
^ \t p+l V tr 

where the elements of rj are series of positive integral ascending powers of t, and 
XI---XP-I have all elements zero save those in the diagonals, which are made up of 
determinate constants ; and X P consists merely of square matrices about its diagonal 
of CD e 2 ... rows and columns respectively, each of which has zero everywhere to the 
left of the diagonal and determinate constants everywhere else. The elements of 77 
are in general divergent. 

The matrix II above will be known as the " determining matrizant." As occasion 
will be found later to discuss a more general matrizant, nothing further will be said 
of it here except for the case in which p = I , which will be worked out fully in order 
to make clear the march of ideas in the more general case. 

12. For p = 1 the equation X ti is an equation of degree e l for 0^, Y fi _! is of 
degree e l I for 0^, and so on. 



-.6(8*)- theiY = 
, <P \Vi ) - u, t i ,,-i 



_ , i 

so that the remaining roots are those of Y^ diminished by unity. 

Similarly the roots of Y I _J are those of Z ei _ 2 diminished by unity, and so on, so that 
the roots of iffi) = are <V, 0, 2 -l, ..., ^"-e.-l. 

The equation 



, i+1 s .r 1 

X, i+a is z^0 1 1 + 2) + .r 1 V(0 1 1 ) + X 1 (0i 1 ) = 0, 

and so on. The equations for y^... are of the same form, with 0^ for 0, 1 . We 
suppose therefore in the first place that #/, 9-?... do not differ by positive integers or 
by zero, so that the coefficients of the first terms in these equations are all other than 
zero, and all the x's and y's are determined uniquely. The quantities a being then 
determined, as above, the solution is altogether determinate. 

If p = l and l l ...0 l ' 1 do not differ among themselves by integers, then the solution 
is of the form 



21 



in which a. i] = 0, unless # 2 * = 





+ + sav 

+3+ y< 



22 MR. E. CUNNINGHAM ON THE NORMAL SERIES 

Now fl (w+cr) = Sl(w)a{Sl- 1 (w)<rQ(w)} (Dr. BAKER, loc. cit., p. 339), and 

~ l , where o = / e ' t 6 ' 1 



and w u is the value of w at t = C, so that 

n(|-4++* 

\^ t' t 

I ,.\-<+e l * \ / /t\ -,'+,' //X-Si'+Si 1 

f /'(f) ' '"A /' a21 (f ' a (f) ' 

/ \t n / \ / \Co/ \ c o/ 

- W O J M //\-9| 2 + , 3 4-1 //\-, 2 + , s 

?.o ,i ....rU - .*" 



I 




there being no exponentials in the last matrix since 

'>' = 0, unless 6>/ = <?/. 

(/I /3 \ /p\ 

-| + )n( -, ), r is a matrix having zero in and to the left of the 
t* 1 1 \t a j 

diagonal, so that Q ( ) has zeros in the same places. 
\t / 

r /r\ 

-gQljj) therefore has zeros in and to the left of the diagonal, and also in the (n 1) 

\ L ' 

places to the right of the diagonal, and also wherever F has a zero, and so on. 

r r 

Thus Q-^Q-^... vanishes after a finite number of steps. Further, none of these 

l> v 

expressions contain log t, since F contains no integral powers of t. 
Thus 

721, 731- 



all the places which were occupied by zeros in F being also occupied by zeros in this, 
and yy contains only a finite number of powers of t, positive or negative, and no 
logarithms. 

We may specify a little more exactly the form of the term y {j . A typical term of 
T/t 2 is 



and Bj0i is not an integer and c,-, is unity or zero. 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 23 

The corresponding term in Q (T/t 2 ) is 



C, -l + A, -l 

L Vw L \to ' 






r r 

It follows that in -g Q -g the r" 1 column is a sum of terms belonging to the indices 

If V 

Q\6i, where ,s- = 1, 2...T, and so for each operation Q. 
Thus finally we have the result 

/r\ 

The term in the i* 1 ' 1 row and/ 1 ' column of H(-a) is a sum of terms belonging to the 

(ft ^ 
-j + ) the / h column is a sum 
t t / 

of terms belonging to the indices l l ...0 l j . 

13. Supposing still that p = 1, let the indices l l ...0 l e * cease to differ by other than 
integers, and likewise the other groups. Let them be arranged in groups differing 
by integers, so that their real parts are in descending order of magnitude in each 
group. 

Then no root of ^(^i 1 ) = will exceed Q* by an integer, and therefore ^(0^ + k)^ k 
a positive integer, so that the equations X f]+ i, ... do not fail to determine x^ 

If, however, 6* = 0i l k, $ (0^+k) ; so that the coefficient of y^ in Y ti+A vanishes, 
leaving y^ unknown. We take ?/// = as the simplest assumption, and the following 
equations then give y l k+\, &c., all without ambiguity. We are, however, left with 
Y tl and Y ei+Jl in general unsatisfied. Of these one can in general be satisfied without 
affecting the rest of the argument by an adjustment of the element x/ 1 - 

It has been seen that a constant a 21 in the matrix xi occurs first with non- vanishing 
coefficient in Y I . 

Clearly, then, if we introduce a 21 t k , it will leave all the equations to Y e]+Jl _i unaffected, 
and add to Y, i+A the left-hand member of Y 6i _j with 0^ + k+l for 6*. 

But Y ! is an equation of degree l 1 of which d* is the greatest root, so that the 
multiple of a 21 added to Y ei+A is not zero. Thus a proper choice of a 21 satisfies Y, 1+4 . 

Again suppose 0* = 0*^ = l l k l k 2 , ^>0, 2 >0. 

Then the equations Z. i+t , Z ti+ , i+ , a fail to give z\, z\ +ki ; but a 31 , 21 can again be 
determined so that, if a 31 * 1+ *% a 3 V' occupy the places above 0^ in XL the equations 
Z. I+AI , Z |+AiH . tj are satisfied, 0^ being unaffected and z l ki , z\ i+tl being taken zero. 

Suppose then l \..0 1 k form the first group of 6^... 6^ differing by integers. Then 
treating the first h columns all in the same way, the ^h(h l) equations Y I , Z.,, 
Z,,-!... must be satisfied identically when the 0^ have been all determined, and must 
be added to the equations of condition already found. 

Suppose now l h * l ...0 l h+k form the next group of roots differing by integers and 
consider the (h + r) lh column r<k. The equation giving 6>, A+I is that indicated by the 
suffix ^-(h+r-l), and those following this up to that with the suffix e l are 
independent of the undetermined elements of r). 



24 MR. E. CUNNINGHAM ON THE NORMAL SERIES 

Further r 1 of the equations subsequent to these fail to determine the appropriate 
element as above, on account of the quantities 1 h+s ] h+r being positive integers 
for s = 1, 2...(r 1). These (1 1) equations are satisfied by putting terms 
< ,* + *- l * +r a A+r,A+*( _ j , i) i n ^ i( wn ile of the other h + rl equations constants 
a* +r '*(s = 1...A) can be found to satisfy h. Thus (rl) equations of condition are 
found from this column, and therefore ^k(k 1) from this group of roots ; and so for 
each group of roots. 

Assuming all the equations of condition to be satisfied, we have now the following 
formal solution 



where ft is as follows : 

The square matrices about the diagonal of h, k... rows and columns respectively, 
corresponding to the groups of 6*... which differ by integers, are of the form 



and all other elements, to the right of the diagonal and within the matrices of e^. 
rows and columns about the diagonal corresponding to the groups of equal roots for # 
are numerical constants, and all others to the left and right of the diagonal are zero. 
Applying now the formula 



the solution is put in the form 




'j ( tjt^j ' ' . . 


\ 




/ 


Cai 


c M ..-\l 




\ 


1 






\ | 


' o, 


(t/t u )~ e ''* *'",... 


_J_ _ 








e... 




1 


i 


i 








/ 
/ 




\ 




I 




/ 




\ , 




/ J 



where in the last matrix all elements are zero that were zero in X i, and c i} is a 
constant if ^-^ is a positive integer, but otherwise is a numerical multiple of t*-*. 

The expansion of the matrizant can be effected as on p. -22, with the result that in 
the. expanded matrix the first h elements of the first row contain Iog(t/t ) to the 
powers 0, 1...A-1 respectively, while the rest of the row is free from logarithms ; the 
second row begins with zero, then unity, and the next (h- 2) elements contain log (/*) 
to powers l...(h-2) respectively, and so on, the A th row being entirely free from 
logarithms. In the (A+l) th row in the k places beginning with the diagonal term 
occurs to powers 0, !...(&-!), and so on. 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 25 

14. Returning now to the general case left out of consideration on p. 16, in which the 
roots of <f>(0 p ) = are not all unequal, we suppose the roots of this equation arranged 
in groups, of which the members are all equal. 

If o-j = or 2 = ... = ov, < ei _i (<TI) = ^-^o-a) = 0, since the roots of <j> ei -i(0) = are 
o- 2 , ...<r r ; and again, <f> fi _ 2 (a 2 ), <ji n _ 8 (<7 8 )...^ (n _ r+1) (<r r _ 1 ) are all zero, where 
$,,-2 = 0....<^> ei _ r+1 = are the equations for dp, 6 P ...6 P . 

The equation for 6 l p --i (p. 16) reduces therefore simply to t|>(cri) = and fails to 
determine 6 l p -i ; but, o-j being already known, this must be merely an " equation of 
condition " among the coefficients. 

Similarly in the equation X, I+2 the coefficient of 6 l p - 2 vanishes, and this equation 
therefore is of the form 

-i, 1 = or _ 1 , = 0. 



Now the operator A p _! acting on this equation, since cri = cr 2 , gives the equation Y f|> 
which, as has been seen (p. 17), is linear in 2 p - l , the coefficient being ^> ei _ 2 (cr 2 ). 

If r = 2, this does not vanish, and therefore X e|+2 is a quadratic for 0\,-i, of which, 
owing to the relation through & p -i, 6 l p -i, 2 p -\ are the two roots. 

If, however, r>2, the equation Y Ei must become an equation of condition, since 
< ti _ 2 (o- 2 ) = 0, and therefore also X ei+2 becomes independent of 6 1 p _ l and gives another 
equation of condition. 

Carrying on this reasoning step by step, we find that X^+i...X, 1+r _j are all 
independent of l p -i, 6 l p - 2 ..., while X fi+r is of degree r in O 1 ^ and independent of 
O l p - 2 .... If any root of this equation be taken for ffip^ the equations Y t] ...Y ti+ ,._ a arc 
independent of 2 p -i, 6 2 P -^..., while Y n+r _ 2 is an equation of degree r 1, which, since 
it is derived from X, i+r by the operator A ;) _ 1; has for its roots the remaining roots 
ofX e , +r . 

Choosing one of these for 6 2 p -i, Z e]+r _ 4 gives an equation of degree ? 2 whose roots 
are the remaining, and so on. 

Similarly, if tr r+1 = ... = ov +s , 6 p - l r+l ...0 p - l r+:i are given as the roots of an equation 
of degree s, and so for each group of equal roots cr. 

Consider now one such group with the values of ^ p _, r+I , ...0 p _ 1 r+ * obtained. 

Let the equations of which these are the roots be 



Then, if the roots of $ s be all unequal, say = TJ...T,, 

^-i(ri)M=0, ^- 2 (T 2 )^=0, .... 
but 

^_ 1 (r,) = 0,/^l. 

The subsequent equations are then seen by the application of A 3 to be 
VOL, CCV. A, E 



2C, ME E. CUNNINGHAM ON THE NOKMAL SERIES 



which, since the coefficients of 8 p - 2 do not vanish, at once give the values of P _/ +1 ... ; 
these, as in the case of P ^ when the o-'s were unequal, can be shown, if the Toots T^... 
undergo a permutation, to undergo the same permutation, so that the same P , 2 is 
associated with any particular T in whatever place this T is taken. 

If, however, the roots T fall into groups of which the members are equal to one 
another, these equations again resolve themselves into equations of condition owing 
to the vanishing of ^^(TJ), &c. ; and, as before, the quantities p - 2 fall into corre- 
sponding groups given as the roots of equations of degrees equal to the numbers in 
the respective groups. 

The process may clearly be carried on as far as the determination of 2 by the use 
of the operators A,,_ 2 ...A 2 . 

A further remark should be made as to the finding of lt in connection with the 
operator A 1( which has been defined to be such that 



Suppose that 2 ...6 2 are given by a set of equations 

a*^ 1 ) = 0, ^(di) = 0, ..., Wl (0/) = 0, 

where the affixes of the w's denote the degrees of the equations, and the roots of each 
equation are the remaining roots of the preceding after any one of them has been 
chosen. 

Suppose that of these 2 ...#/ are equal, so that 



Then 6,^(0;) = 0, o,*_ a (0 a 8 ) = 0, ..., w ,_ A+] (0/-i) = 0, but <o,_ A (0/) =/= 0. 
Then if the X equations following u> k be denoted successively by 

i* = 0, 2 w,t.= 0, ..., 

i(a k is independent of x^, &c., by virtue of &>* = and the preceding equations, and 
therefore 

Aid*,) = *_(#) 0, since 0J = P >, 0^ = 0^, ..., 

so that ,o) A is also independent of 6? and must therefore vanish identically when a l is 
determined. Hence also 2 o> k is independent of*! 1 , &c., and therefore 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 27 

But in the same way 

so that !<*_! (0 2 2 ) must also vanish when 0./ is found and thus iw A _ 1 (^ 2 1 ) == 0, so that 2 a> k 
is also independent of 0^. 
Ultimately we have 



and o> k _ h (0 2 h ) = and is independent of 0f. 

Thus h G> k (Oi] is an equation of degree h for (V, since 0% = 2 h , 3 l = 3 h .... 

Suppose its roots are v lf v 2 , ... v h - 

Take 6 to be v^ Then A-IW*-! is an equation of degree h l for 0*, and its roots 
are (p+v a )(p+v a )..., as shown by effecting the operation Aj. 

Choosing one of these again to be 0*, say p + v 2 , A-aw*-a is an equation for 0, 3 , whose 
roots are (2p + v s ), (2p + v 4 ).... Thus the quantities l l ...0 l ' 1 are r 1( (_p + r a ), (2^+r,)..., 
(h-l)p+v h . 

In order to particularise the order of the roots v 1} v 2 , ..., they are arranged as soon 
as found as follows : 

Let all those roots which differ from one another by integers be grouped con- 
secutively and let the arrangement in each group be such that 6 r ~ l 9 r = or a 
positive integer. Suppose, now, the equation k (a k (0i l ) = is the equation X ? . 

Then the coefficient of x in X ?+1 is A w /l (# 1 1 +l) which, since no root of A w*(0) = 
exceeds 0, 1 by a positive integer, does not vanish. X 7+1 is moreover independent of 
x a l , ..., owing to the equations k -i<a k = 0, ..., being satisfied independently of 0,\ 

Thus X ?+1 determines x^. 

Similarly, X ?+2 gives x a l , the coefficient being A w A (0 1 1 + 2), and so forth. 

Of the Y equations, that determining 0^ is obtained from X 7 by the operator A t . 
It is, in fact, Y ? _ p . 

The coefficient of y^ in Y^.^+j is equal to the coefficient of o^ 1 in X ? _ /)+1 with 0^, 
0./, ..., substituted for 0^, 2 l , ____ But X ? _ p+1 vanishes identically as far as 0^ is 
concerned and 2 , ..., are the same as 0^, .... Thus Y g _ p+1 is independent of?/! 1 . 
Similarly, Y g - p+2 ...Y q - l are all independent of the undetermined elements of y. 

Suppose now 0\0i X (a positive integer). 



The equation Y ?+ft contains y^, ..., y k , the coefficient of the last of these being 
A eo A (0! 2 +&) which vanishes for k X. 

If, now, in the matrix *%r( r = P> P~ 1--.2) the second element of the first row be 
c r 21 , and in ^ be c 21 ^, the constants c will, as before (p = 1), affect first the equations 
Yj-p+j..^.! and Y ?+A respectively, entering into these with non- vanishing coefficients. 
Let c r 21 be determined then to satisfy the first pl of these equations; Y ?+1 ...Y ?+x _j 

E 2 



2 8 ME. E. CUNNINGHAM ON THE NORMAL SERIES* 

then give ^...yV-i. Y, +A then fails to give y,\ but c 21 can be chosen to satisfy the 
equation and y? may be taken zero. 

The following equations then give the remaining elements in succession. 

This leaves the equation Y, in general unsatisfied, and a further equation of 
condition is therefore necessary. 

Similarly, if 0,"-0, 8 = fi (an integer) of the equations Z, we can, by proper choice 
O f C 32( r _ ,...2), satisfy the p-l following that which determines 6^, viz., Z,-^ ; 
and just as a proper choice of the constants o r 21 enabled us to satisfy Y g - p+1 ...Y q -i, the 
constants c r 31 can be chosen to satisfy Z f _f+i...Z 2 -i. 

Thus two equations, Z,, p , Z g , are left unsatisfied in general. The two remaining 
constants, c, 32 and c?\ are utilised to satisfy the equations Z, +(1 , Z ?+A+ ^, in which the 
coefficients of z* and z\ +li vanish respectively. To do this the terms c 31 ^" and c**"*' 
are inserted in the third column of Xi- 

If then the indices O^.-.B,' be equal, or differ from one another by integers, exactly 
similar treatment applies for each of the first I columns of 77, the i ih column furnishing 
(i 1) equations of condition. 

For the (Z+l) tlh column, however, 1 r -0 1 ' +1 , (r^h) is not equal to zero or a positive 
integer. Thus h w k (&i +l + m) does not vanish for any value of m, and the Ip constants 
c r l+l ''(r =p...l, s = l...l) can be determined to satisfy the Ip equations between 
Uq-,,, and Uj+1, U denoting an equation of the l+l" 1 column, and, in particular, ~U g -i p 
being the equation determining 0/ +1 and U ?+1 determining u^. 

For the next column, however, l l+l 1 l+i may be a positive integer, X 1 say, so 
that h <a k (# 1 ' t+2 + V) = 0, and the (</ + X 1 )"' equation, instead of determining the 
appropriate element of >?, can only be satisfied at the expense of the 5 th , by making 
the element above 9^ in ^ c' +2 ' m ^'. The </ th equation then becomes a further 
equation of condition. Thus we shall obtain r 1 equations of condition from the 
(/ + r) th column, associated with an index belonging to the second group of indices ^ 
differing among themselves by positive integers ; and so on through all the indices as 
far as #/'. 

A similar treatment is now applied to the columns (h+l)*,.(h+k), for which 
0/' +1 = e r h+2 . . . = 6 r h * k (r = p. . .2) ; 6V l+1 is given as the root of an equation of degree k ; 
and the minors of the determinants % whose diagonals are r h+l ...6 r h+k , have the 
elements to the right of the diagonal suitably adjusted as above, while one equation 
of condition is furnished in connection with every difference 1 * +r -r# 1 A+s , which is an 
integer. 

Supposing these equations all satisfied, consider the expansion of the matrix 

--- + }> which is effected in just the same way as for p = 1 (p. 22). 



P + l Q 

If to = 2 p where Q r is a matrix made up simply of the diagonal terms r 1 ...0 r ", 
the application of the equation 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 29 

o (tv+<r) = n (w) n [rr 1 (w) o-n (w)] 

resolves the required matrix into a product of two, of which the first, 11 (w), consists 
simply of diagonal terms of which the r th is 



The second matrix has zero everywhere in and to the left of the diagonal ; and, 
since in the matrices ^ the element in the r th row and s th column was zero unless 
m = Q m ' '' (m = p+l, %), it contains no exponential expressions. It can therefore be 
completely integrated in finite terms, just as was done in the case p = 1 (p. 23). 

15. A simple example may be appended of the application of the method to a particular system. 
Consider the equation 

Putting iji - y, y, = y?y\ we have the linear system 

y'=t o, 



= 17 l }L+( Q 'U+/ \~L 

The characteristic equation is 

-0 or 



-P, -S-p 

giving equal roots - 1 for p. 

With p = ( j the transformed system becomes 

OM./O . 



= uy say. 
Considering now the subsidiary equations 



Then the equations to be satisfied are 

II. (1) xj - (1 + #1) *i l = '2) (2 - 61) x -1=0, 

I. and II. (2) give (6!- 1) 2 = 0. 

We take 9\ 1 therefore, so that a^ 1 = 1 and x-2 = 2xi l . 

Again 

III. (1) xo? - &i zj 2 - 0, (2) (1 - 6>,) xj - a, 1 = 0, 

of which (2) gives Xi l = 0, so that x = 0. 



30 ME. E. CUNNINGHAM ON THE NORMAL SERIES 

Similarly x l * = xt* = Q, and so on. 

The equations for the second column are 

I. (1) y 2 1 -i 1 -X = ) (2) 3-0 2 -Zi 2 = 0, 
(2) gives 2 = 2 = 1 + 0i and (1) gives J/2 1 = A. 

II. (1) yj - (\ + O a ) yi l - z, 2 - A- xS = 0, (2) (2 - 0,) yj - xf - W = 0, 
(2) gives A. = and (1) gives y? = 2yJ and also yj = 0. 

III. (1) y? - %! 2 - zi 3 - W = 0, (2) (1 - 6 S ) </2 2 - 2/1 1 = 0, 

so that yi 1 = and ?/ 2 2 = 0. 

It is easily seen that all the remaining terms vanish. 
Thus the solution reducing at x = x to the matrix unity is 

1/1 o\\/i o\-i 

2J/U V 



where 



Thus 

fl 




f n r /o i\ 

T-lo *- tt o ^ bo oj 





16. The number of conditions found in the course of the analysis shows that the 
solution in this form which may be called the " normal" form, by analogy with the 
name "normal integrals" of linear equations is by no means always possible. As 
many writers have pointed out, there is a much more general type of solution than 
the normal series for the ordinary linear equation, in the form of a normal series in a 
new independent variable x 1 '*, k being a positive integer (CAYLEY, HAMBUBGER, 
FABKY, &c.). 

The method developed in the foregoing is peculiarly adaptable to the investigation 
of these integrals, inasmuch as the transformation to a new independent variable is 
very simply efiected. 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 31 

If in the linear system 

-| = u (t) y we put t = (j>(z), 

we have without any calculation the new system for y as a function of 2 



Suppose now (f>(z) = z k . Then the transformed system is 



If, then, the original system is of rank p, so that 



the new system is 

dy Vka^_ Jca ,_ 

+ - + - 



and is of rank kp. 

If, now, we were to put z = F' 1 *'' . z 1 , the form of the equation would be unchanged, 
while the coefficient of z i;!cp+l in the right-hand member would become the original 
canonical matrix a. p+l . This is, however, not necessary, as the whole investigation 
could be carried out equally well if any constants whatever replaced the unities to 
the right of the diagonal in a p+1 . 

It may now well happen that though all the equations of condition found for the 
general system are not satisfied, those associated with the new system are all satisfied, 
so that the new system possesses a solution in normal form. If this is so, the original 
system will be said to admit of a solution in subnormal form. In fact, an integer k 
can always be found such that this is so, owing to the vanishing of the coefficients of 
z -*f+r{ r= 0) !...(_ 2)}. 

In the first place, all the conditions arrived at from the equations X,, Y,, ... will 
be satisfied (p. 13), for the coefficient of z~ kp is identically zero; in general, the 
left-hand members of X,, Y r . . . are rational integral functions of the elements of the 
matrices A^, A^-j, ..., A tp _ r+1 , if A, n stands for the matrix multiplying z~'", and 
contain no term independent of these elements. 

Now the conditions found on p. 13 arise from the equations Xj.-.X,,-!, Y^-.Y^-a, ..., 
and therefore involve the matrices A^, ..., A A? _ ei+2 . These conditions will therefore 
all be satisfied if k > ej. Similarly, the analogous conditions for the second group of 
equal terms in the diagonal of a p+1 will be satisfied if k ^ e 2 , and so on. 

Consider first, as being simplest of explanation and as containing the essential 
features, the case in which all the roots of the characteristic equation are equal, so 



32 ME. E. CUNNINGHAM ON THE NOEMAL SERIES 

that E! = n. It will be shown that a subnormal form satisfying the equation certainly 
exists if a/" i= with k = n. 

We know from the foregoing investigation that 6\ p is given as the root of an 
equation of degree n, and that, if the roots of this equation are all different, no more 
conditions than those just mentioned as satisfied are necessary to ensure the existence 
of the subnormal solution. But in this case the equation for 0\ p is particularly easy 
to construct. We have, in fact, 

nxf-0 1 ,, = 0, x? = xf = ... = a," = 0, 

nxf-ffi^' = 0, ir a = ... = x = 0, 

nxS-ffinStf-ffiv-M* = 0, xf = ... = x s = 0, 



r n Q\ n-l_f)2 -l _ A 

X B _i U ,, p Ji n -2 " np&n-X ... - U, 

u ,,, i x n n - l .. . + A n ( p _])+i = 0, 



from which at once we have 

-+I - u ' 



Tlius, unless A ln B(p _ 1)+1 = 0, the values of 6 l n) , are all different, and a solution in 
subnormal form is therefore possible, as stated above, with the independent variable 
changed to x i;n . 

If, however, A 1 ",,^-]^] = 0, we have 

(n _ _ tin _ f\ 

\J n p ... -- I/ n p - U, 

and it will be found that the same conditions are necessary between the constants 
A.n(p 1)+1 as were found previously (p. 13) between the constants ot p , A n(p _, )+1 
being the same as n . a. p , e.g., from the equations 



- 1 .^,,*, = 0, A. 2 '\ (p - l)+l -nx n = 0, 
we have 

1 Mp _ 1)+1 = 0, i.e, a p 2 ' n + a p 1 '"- 1 = 0, and so on. 



Consider now what happens when these conditions are not all satisfied. Suppose, 
for instance, a/^ + a/'"- 1 ^= 0. Let the original system be transformed by the change 
of variables 



Then from the equations 



= z k , k = nl. 



, (? ,- 1)+1 2, 2 = 0, 
we obtain the equation for 6 l kp 



SATISFYING LINEAR DIFFERENTIAL EQUATIONS. 33 

(&\p) n -^fo (A'."-^ _ 1+1 + A 2 '". _ ) = 
K" Ic 

and since the last written coefficient is not zero, the roots of this equation are all 
different, and therefore the transformed system possesses normal integrals free from 
logarithms. 

Again, suppose a. p <n = and that a. p l -*~ 1 + a. p * 1 also vanishes; then the roots of this 
equation all become zero, and we find that the condition a. p ' n ~* + a. p ' n ~ l + a*' n = is 
also necessary. If this is not satisfied and the original system be transformed by 
x = 2*, k = n 2, the equation for 6 l Kp becomes 

ai \ //}i \2 

V kp\ I u kp \ ( \l,n-2 , A 2 '" -1 J. A :! . " x 

i I ~~ r~ I \- a - Dtt-sm-r-tt- (/t-2>+i + - rt - : 



p(k-2) + \ ~ V> 

which has two zero roots and the rest all different. If the one condition necessitated 
by the equality of the two zero roots is satisfied, the solution is again found. If this 
condition is not satisfied, the transformation z = effects what is required. 

Suppose now all the conditions of p. 1 3 are satisfied. Then whatever value of k be 
taken, we have 6\ p = 0, so that, as fur as we have seen, the transformation does not 
render the solution any nearer. 

We must, in fact, proceed to consider the further conditions for the case when the 
roots Op are equal (p. 13). 

Suppose, for instance, the first of these conditions is not satisfied, then putting 
k = n, we shall have 9 l kp = ... d" Kp , the conditions then necessary before the deter- 
mination of Oty-i will be satisfied, and we shall eventually obtain a binomial equation 
for 8 kp -i of degree n in which the constant term does not vanish ; the roots of this 
equation being all different, the subnormal integral exists. 

Thus we may go through all the equations of condition in turn. 

In the more general case, where the roots of the equation for 6 P fall into more than 
one group of equal roots, the procedure is exactly similar. 

For example, suppose that a. p '*\ a/ 1 " 1 " 1 '' 1 ' 1 '' 4 , ... are all different from zero. Then the 
preceding work suggests that a solution may be ftnind in which the first e l rows- 
proceed according to powers of ' % the next e 2 according to powers of i; ' a , and so on. 

The whole would thus be of normal form with the variable t lik , k being the least 
common multiple of e^ e 2 

In fact, if we change the independent variable to t llk , k having this value, the matrix 
A ip -, 1+ i is identically zero, and the indices G^p.-.O'^ are the roots of (^)'' + = 0. 

These roots are all equal, and the corresponding equations of condition are all 
satisfied owing to the vanishing of the matrices other than A A . r+I . 

If, now, we form the equation for #%,_! we have 



T. v 2 ffL _ Z 3_f)l 2 _ A 

KX 2 V k p -\ U, /CX 4 (7 Ap-l.t-2 - - U, 

~" /cp-l X "2< l -2 + A ''kp-2^ + 1 = 0, 

VOL. CCV.^ A. P 



34 ME, E. CUNNINGHAM ON THE NORMAL SERIES 



If - = 2, A. l \. p - 2ti+l = k.ct p> and therefore if a p le ' ={= 0, the ej roots of this equation 
are all different. If, however, - > 2, A*p_ 2ei+1 again is identically zero, and the 

necessary equations of condition are again satisfied. 

Proceeding thus we find, in fact, that if a p fl ^ 0, 6* kp) ..., 6' kp -k,^i', s = l.-.ei all 
vanish and that &\- p - kei +i is the root of a binomial equation of degree e 1( whose roots 
are all different, and so for the other divisors of k. If, however, a. p ' 1 = we have the 
same equations of condition again necessary, viz., a/' 1 and a/'' 1 " 1 = 0, &c. 

Assuming, then, that a p lt > ^ 0, we find, without difficulty, that all the quantities 
9* vanish for s = I...e 1; save those for which r is of the form k(pm/e 1 ) + l, so that 
the exponential arising in the first ej rows involves only ?*'> and not t llk . 

The discussion of whether the solution of the subsidiary equation proceeds according 
to powers of t l! ' 1 only in the first EJ columns will not be carried out in full here. It is 
enough to know that, provided a,,' 1 ' 1 , a / / 1+1 ' <r '" ) " < - do not vanish, a subnormal form 
certainly exists satisfying the equation. 

If, however, one or more of these quantities does vanish, and one of the consequent 
equations of condition is not satisfied, we may, as on pp. 31-33, find a new integer /-, 
such that the necessary conditions for the existence of the subnormal form are 
satisfied. 

17. As a concluding example consider the system derived from the equation of third order and rank one 

Clsot 3 + Cl 3 iZ 2 

~ ~ .'/ T 
which with 

gives 

if-' 

I " \ / Z 

.\-oss -a-2-2 O/ \~0ss -BO, 4/ \-fflgi - 20 O/ \-a 30 0; 

The characteristic equation is - p 3 - pa?, + a 33 = 0. 

We shall confine ourselves to the case in which this equation has three equal roots. These must all 
then be zero, and a = 0, a 33 = 0. 

For the equation then to possess a normal solution we must have 001 = 0, a 32 = 0. Supposing these 
conditions not satisfied, put z = t 3 ; then the equation becomes 

1 ON / O v 

! 1 I 

\ - a 3 > - 0-21 4/ 
The subsidiary equations then become 

= 0, 3x. 2 s - OJxi* = ; 

i - (9,1 = 0, 3 3 3 - OJx-p - O^XT? = 0, - ^ 3 1 // - O'Sxi 3 - 3a 33 = 0. 









.'/ T- - 


-4 







y = v, 
















yi = 


y, -y, ys=.Y' 












/ 





1 


\, / 





0\ / 





\ / 



















i* 





2 oU+l 

1 > 





oU/ 

+ 













SATISFYING LINEAE DIFFERENTIAL EQUATIONS. 35 

The last gives - ,', (0s 1 ) 3 - 3 32 = 0, so that 6*3!= - 3(rc 32 )S, where any cube root may be taken, the other 
roots giving # 3 2 , 3 3 . 
Further 

3z 4 2 - 3 W - Wx - (1 + <V) .-Ci 1 = 0, 



3/4 3 - flsW - Wtf + (1 - 01 1 ) Zj2 = 0, 

- tfsW - ^2 S + (3 - 6V) ;,8 - SasaKi 1 - SoziX; 8 = ; 



of which the last gives 

-fcV.fW-aaieV-o, 

so that ftj 1 = 2i/(8o)J, and #.r, 0o 3 are given by taking the other roots for ( 32 )*. 

Lastly the equation 

- # 3 W - foxa 3 + (2 - 6V) z 2 3 - 3a 82 a; 3 i - 3a. n xJ = 
gives 



,3 

which gives 



so that 6' 1 1 = 5. Similarly, 0, !i = 1 8 = 5, and a subnormal form exists satisfying the equation, of which the 

>'/ _ _f^]_ 

first column has the determining factor c 2 -' " ;E '' tS, and the 'other columns have the same factor with the 
other cube roots of so. 

We may remark that this agrees with the results obtained for this equation by the ordinary methods 
(FoRSYTH, "Linear Differential Equations," 99) under the assumption that 32 =^0. We have shown 
that this is a necessary condition for the existence of the subnormal form in the variable /- ,~S satisfying 
the equation formally, unless we have also <i 21 = 0. 

If, however, 32 = and n^i^O, then, as we have seen above, the transformation / = il will give us a 
system admitting of 3 normal solutions; the equation for 0\ is, in fact, (#i) 3 - 4 2 ]0i = 0, giving } =0 or 
2rt 21 *. 

We see, in fact, that, when (130 = and ff-Ji^O, the characteristic index of the original equation is 2, so 
that there will be one regular form satisfying the equation, i.e., an expression of the form ./- P P (./ X 

If a 3 v, a 2 i ar c both zero, the equation is of Fuchsian type. Thus the normal or subnormal forms are 
found in all cases. 



F 2 



C 37 ] 



II. Memoir on the Theory of the Partitions of Numbers. Part III. 

By P. A. MACMAHON, Major R.A., Sc.D., F.R.S. 
Received November 21, Read December 8, 1904. 



SINCE Part II. of the Memoir appeared in November, 1898, the following papers by 
the author, bearing upon the Partition of Numbers, have been published : 

" Partitions of Numbers whose Graphs possess Symmetry," ' Cambridge Phil. 

Trans.,' vol. XVIL, Part II. ; 
" Application of the Partition Analysis to the Study of the Properties of any 

System of Consecutive Integers," 'Cambridge Phil. Trans.,' vol. XVIII. ; 
"The Diophantine Inequality KX^/JHJ," 'Cambridge Phil. Trans.,' vol. XIX. : 
" Combinatorial Analysis. The Foundations of a New Theory," ' Phil. Trans. 

Roy. Soc. London,' A, vol. 194, 1900. 

In the present Part III. I consider problems of " Arithmetic of Position." In 
particular. I define a " general magic square " composed of integers and show that for a 
given order of square it is possible to construct a syzygetic theory. Such a theory is 
worked out in detail for the order 3 as an illustration. I further discuss the problem 
of the enumeration of the squares of given order associated with a given sum. I show 
that there is no difficulty in constructing a generating function for such squares even 
when the construction is specified in detail, and I obtain an analytical expression for 
the number when the sum, associated with rows, columns and diagonals, is unity 
or two. 

9. 

Art. 124. A "general magic square" I take to consist of n 2 integers arranged in a 
square in such wise that the rows, columns and diagonals contain partitions of the 
same number, zero and repetitions of the same integer being permissible among the 
integers. 

An ordinary magic square I define to be a general magic square in which the n 2 
integers are restricted to be the first n 2 integers of the natural succession. 

We may regard general magic squares as numerical magnitudes. To add two such 
magnitudes we add together the numbers in corresponding positions to form a 

VOL. CCV. A 388. 30.6.05 



38 MA JOE P. A. MAcMAHON: MEMOIE ON THE 

magnitude which is obviously also a general magic square. We can, therefore, form 
a linear function of magnitudes of the same order, n, the coefficients being positive 
integers, and such linear functions will denote a general magic square. 

The magnitudes, of the same given order, can be taken as the elements of a linear 
algebra, and since arithmetical addition can be made to depend upon algebraical 
multiplication, the properties of the magnitudes can be investigated by means of a 
non-linear algebra. 

Art. 125. The properties of a general magic square can be exhibited by means of 
homogeneous linear Diophantine equations, and it thence immediately follows that 
there must be a syzygetic theory of such formations. There exists a finite number of 
ground forms, corresponding to the ground solutions of the equations, and the method 
of investigation determines these and the syzygies which connect them. 

Generally speaking, there is a syzygetic theory associated with every system of 
linear homogeneous Diophantine equalities or inequalities, and it is because invariant 
theories depend upon such systems that they are connected with syzygetic theories. 

Art. 126. The method of investigation about to be given applies not only to magic 
squares of different kinds but to all arrangements of integers, which are defined by 
homogeneous linear Diophantine equalities or inequalities, whose properties persist 
after addition of corresponding numbers. 

For example, the partitions of all numbers into n, or fewer parts, are defined by the 
linear homogeneous Diophantine inequalities 

1 >:a 2 >a : ,...5:a,,, 
and if another solution be 

A=&>&. ..==&, 

we have 



and since the property persists after addition, a syzygetic theory results. 

This is one of the simplest cases that could be adduced and is at the same time the 
true basis of the Theory of Partitions. 

Many instances of configurations of integers in piano or in solido will occur to the 
mind as having been subjects of contemplation by mathematicians and others from 
the earliest times. These when defined by properties which persist after addition of 
corresponding parts fall under the present theory. 

Art. 127. There is no general magic square of the order 2 except the trivial case 
a a 

, but we may consider squares of order 2 in which the row and column 

Cf Ct 

properties, but not the diagonal properties, are in evidence. 
Let such a square be 



2 

a* 



THEORY OF THE PARTITIONS OF NUMBERS, 
which must clearly have the form 



a, a, 



! 2 1 

and we may associate with it the Diophantine equation 



and regard a,, 2 and a 5 as the unknowns. 

The syzygetic theory is obtained by forming the sum 



for 



all solutions of the equation, and the result is 

i 



l_ 

a' 



auxiliary quantity and the meaning of the prefixed symbol fi is that 
n of the algebraic fraction in ascending powers of X,, X a , X 5 we are to 
rms only which are free from a. 



Where (6 IS an ctLi^vmc^i y vjucmuiuy CHAH LUC meet 

after expansion of the algebraic fraction in as 
retain those terms only which are free from a. 
The expression clearly has the value 

1 

i-x^.i-x-X 

denominator factors denote the ground solutions 



The 



1 


a a 


5 


1 





1 





1 1 



and the absence of numerator terms shows that there are no syzygies. 
Thus the fundamental squares are 



1 
1 



1 

1 



and this is otherwise evident. The case is trivial and is introduced only for the 
orderly presentation of the subject. 

Art. 128. Passing on to the general magic squares of order 3 we have the square 











40 MAJOE P. A. MACMAHON: MEMOIE ON THE 

defined by the eight Diophantine equatious 



= a !0. 



= a io- 



We require all values of the quantities a which satisfy these equations. 
To form the sum 



for all solutions, introduce the auxiliary quantities 

ft, b, c, d, e, f, f/, h 

in association with the successive Diophantine equations. The sum in question may 

be written 

1 



_ 
f (1 -adgX,) (I -fU'X 3 ) (1 -rt/'AXs) (1 -MX,) (1-beghXJ 



where after expansion we retain that portion only which is free from the auxiliaries. 
Remarking that 

1 1 



we eliminate the auxiliar ft and obtain 

1 



l_p222)/l_^*L)/i- 



Put now bd = A, be = B, If- C, cd = D, and we obtain 

1 






f/ AX.X.pW X^W. X 3 X 

"BOD&A era/ 1 



(1 -Br^X,) (1 -CX,) (1 -DAX 7 ) (l -^2) f 1 - CD fM 

\ A / \ A / 

an artifice which reduces the number of auxiliars to be eliminated by unity. 



THEORY OF THE PARTITIONS OF NUMBERS. 



Remarking that 



(l-P 1 P 8 )(l-P 1 P 4 )(l-P 3 P a )(l-P 2 P 4 ) 
1 



(i-p 1 p 4 )(i-p s p 8 )(i-p s p 4 ) 

We eliminate A and find 



ft 



^1-4 X.X.X.o ) (1 -BDX 4 X S ) ( 1 -CD?X 4 X,) ( 1 - ^ 7 X 2 X U 

\jLs(f/t 



-Br///X s )(l- 

1 



i \ / / 

1 "VVY lit ,/VVV \ / l TJTiV V \ / i l V V 

1 TTT AiAsAjo I ""TOT AjAoAn, (1 .DlJA.,A 8 ) l ~ 7TST~r -^-a-^-io 
C/i B nrk^j, 



- - X 3 X 1U (1 -B^X 6 ) (1 -CX H ) (1 -DAX 7 ) 



Eliminating B from the first fraction and C from the second, we have 

n l 






( (} ODoX^^i n;,Y_\/i Y Y \ /i ^' YYY V 


1 i~\ PY \ 

l (1-UA 6 ) 


l~\ ^< 2 Y YYY \ M YYYY 1 
i * ~9 AiAjAoAjoJ 1 1 - A 3 A 4 AgAjo 1 

gD xxxxx 

/; 





-CD<7X 4 X 9 ) (1 - 



~~rm~7 XjXj 



(1-CXe) (1-/X 1 X B X 9 X 10 ) ( l - - 

tS 



1- 

k 

VOL. CCV. A. 



/ 1 T^Ti Y \ i 1 "V V AT Y i 

1 1 ~~ J-'/i-A.j ) II A.J AgJi.gA.jQ I 



G 



41 



42 MAJOR P. A. MxcMAHON: MEMOIR ON THE 

From the first fraction eliminate C, from the second C, and from the third B, 

obtaining 

1 



I 



(l-D/iX 7 )(l- 



l - 



l - - X 3 X 4 X 8 X 10 ) ( 1 - 1 X 2 X 4 XX 10 
9 / \ " 



+ fl 



T A1 



'j X^jA^XgXnj 



-<7%X 6 X 9 X 1U ) 1 - X 3 X 4 



X 2 A ( jX ]u 



1 Y ^ 

/I " 



(1 (r/XiX 3 X 4 X 5 X 8 X 9 Ajo ) 



-D/.X 7 ) 1 - -2 X 1 X 4 X 8 X 9 X 1 



X 2 X 6 X, 



i 



1 - 1 X 3 X 4 X 8 X 10 ) ( 1 - 1 



L (l-^X 3 X 6 X 10 j(l- 

Eliminating D from each of the three fractions, we obtain 

1 



(1 -/ 



1 - 



1^ 
9* 

I' 



-X S X 4 X 8 X 1 



1 \ / 1 

1 -A^-X^Ay-X^o 1(1 -A. 3 X4-X 8 X 10 
tj ' i/ 



1 ^ / 1 * 

1 j X 2 X 4 X 9 Xi ) ( 1 ^- 2 X ] X 2 X 4 X 6 X 8 X 9 X 10 ) 

fl I \ II / 



T-Xj 



(1 X 1 X 2 X 3 X 4 X 5 X fi X 7 X 8 X 9 X lu ) 



(i -f/^x. 

(1-A 2 X 3 X 8 X 7 X 10 ) fl-ix i 



i - Ix 2 x 6 x 7 x 10 ) (i - Ix 3 x 4 x 8 x 

ts * \ y 



111 



THEORY OF THE PARTITIONS OF NUMBERS. 



43 



Art. 129. Before proceeding to eliminate g and h, observe that if we now put 
g = h = 1, we obtain the generating function for the solutions of the first six of the 
Diophantine equations corresponding to the squares which possess row and column 
but not diagonal properties. 

Putting g = h = 1 , the generating function reduces to 



X 1 X 5 X 9 X 10 ) ( 1 X 1 X 8 X 8 X 10 ) ( 1 



^io) (1 X 3 X 4 X 8 X 10 ) (1 



(1 
indicating ground forms 



connected by the ground syzygy 

. X 3 X 4 X 8 X 10 = 




X 1 X 6 X 8 X 10 , 



X 3 X 4 X 8 X 10 , 



corresponding to the fundamental squares 





100 




010 




1 




010 




1 




1 




001 




1 




1 




1 




1 




001 




001 




1 




010 




010 




001 




1 


connected by the fundamental syzygy 




100 




1 




1 




010 


+ 


1 


~r 


100 




1 




100 




010 




100 




010 




001 


= 


1 


+ 


001 


+ 


1 




1 




100 




100 


each side being equal to 




1 1 1 






1 1 1 


. 




111 





Ill 



This is the complete syzygetic theory of these particular squares of order 3. 

G 2 



44 MAJOR P. A. MACMAHON: MEMOIR ON THE 

Art. 130. Resuming the discussion, we proceed to eliminate </ and h and remark 
that the second fraction may be omitted as contributing no term free from h. 
Eliminating g from the first and g from the third, we have 



,, 



i Y Y 2V 2v v 2V v 3\ /i Y Y 2 Y Y 2 Y 2 Y Y 3 \ 

L AjAg A 4 A5A 8 AgAjQ J ^ 1 AjA 2 A5A<j A 7 A 9 Ajy J 

(lh X 3 X 6 X 7 X 10 ) ( 1 j- X 2 X 4 X 9 .A 



aV 2V 2V 2V 2V aV 2V 2V 2V 2V 
Aj A 2 A 3 A 4 A 8 A B A 7 A 8 A 9 A t 

r '' V V 2V 2V V 2V V 3\ /l Y Y 2 Y Y 2 Y 2 

Aj A 3 A 4 A 5 A 8 A 9 A 10 ) (i A! A 2 A 5 A 6 A 7 

(1 h X 3 X 5 X 7 X 1(I ) ( 1 Y XiXtfXaXio j ( 1 j- 2 X 1 X 2 X 4 X )) X 8 X 9 Xi 

Art. 131. If the diagonal property associated with (j is alone to be satisfied in 
addition to the row and column properties we may put h = I. Observe that the 
second of the three fractions cannot now be omitted. Simplifying we obtain 

1 V 2V" 2V 2Y 2V 2V 2V 2V 2V 2V 6 
AI A 2 A 3 A 4 A 5 AK A 7 A 8 A 9 Am 

( L XiXgXgXio) ( I X 2 X 4 X 9 Xn,) (l X 3 X 5 X 7 X 10 ) 

II V V 2V V 2V 2V V .1\ /I V Y 2Y 2Y Y 2V Y 
. ^ i ^-1^-2 ^-5-^-6 A 7 A 9 A ll( ; ( I A t A 3 A 4 A 5 A 8 A 9 A 

Establishing the five ground products 



X 3 X 5 X 7 X UI , 

XY 2 Y Y 2 Y 2 Y Y :! 
!A 2 A 5 A 8 A 7 A 9 A, , 

XV 2V 2V V 2V V :t 
lA 3 A 4 A S A 8 A 9 A 10 

connected by the ground syzygy 

(X 1 X 6 X 8 X 10 ) :J (X 2 X 4 X 9 X 10 ) 2 (X 3 X 5 X 7 X 10 ) 2 
= (X 1 X/X 5 X, 2 X 7 a X 9 X 10 3 ) (X 1 X/X 4 2 X 5 X/X 9 X 10 3 ) 
corresponding to the fundamental squares 

100 010 001 
001 100 010 
010 001 100 

1.20 102 

^012 210 

201 021 



THEORY OF THE PARTITIONS OF NUMBERS. 45 

connected by the fundamental syzygy 

100 010 001 

2001 +2100+2010 

010 001 100 

120 102 

= 012 + 210, 
201 021 

involving the complete theory of the squares in which the property of one chosen 
diagonal is excluded. 

Art. 132. Resuming and finally eliminating h, we obtain 

7l Y Y 2 Y Y 2 Y 2 Y Y 3\ /i Y Y 2 Y 2 Y Y 2 Y Y s \/i Y 2 Y Y 2 Y Y Y 2 Y *\ 
\ L -A-i-Aa A 5 Afl A 7 A 9 A 10 ) {L A,A 3 A 4 A 5 A 8 A 9 Aui } (L A 2 A ;! A, A 5 A 7 A 9 A 10 ) 

X2V V V 2V V 2V 3/1 V 2V 2V 2V 2V 2V 2V 2V 2V 2V *i\ 
l AsAgA^ A 7 A g A 10 ^ J A t A 2 A :i A, A, s A H A 7 A 8 A., AH, ) 

"~ l~\ Y Y 2 Y Y 2 Y 2 Y~Y 3\ /i Y Y 2 Y 2 Y Y 2 Y Y *\ 
V 1 -A.j-A.ji A 5 A 6 A 7 A 9 An, ) ^1 AjA 3 A 4 A S A 8 A 9 An, J 

aY 2 Y Y Y 2 Y Y 2 Y 3 \ /I Y Y Y Y Y Y Y Y Y Y :(1 
Aj AgA 5 Afl A 7 A 8 A 10 ) (i A 1 A 2 A 3 A 4 Ar,A H A 7 A 8 A 9 A ll , ; 

which may be written 



a Y 2 Y 2 Y 2 Y 2 Y 2 Y 2 Y 2 Y 2 



(1 XjX 2 XgXtf Xj XjX 10 ) (1 X^g X 4 'X 6 X 8 XflXin' ) (1 Xj X 3 X 5 X H X 7 X 8 X ln ') i 
( 1 X 2 2 X 3 X 4 2 X 5 X 7 X9 2 Xi 3 ) ( 1 X 1 X 2 X 3 X 4 X 5 X B X 7 X 8 X 9 X 10 ) 
indicating the ground products 

XY 2 Y Y 2 Y 2 Y Y 3 
lA 2 AsAg A 7 A 9 A 10 , 

Xv 2V 2 Y Y 2 Y Y 3 
lA 3 A 4 A 5 A 8 A 9 Ai , 

X 2 Y Y Y 2 Y Y 2 Y 3 
1 A-sAgAg A 7 A 8 A 1() , 

X 2 Y Y 2 Y Y Y 2 Y 3 
2 A 3 A 4 A 5 A 7 A 9 A 1() , 

Xj X 2 X 3 X 4 X 5 X 6 XjX g X9X 1 i|' 

connected by the fundamental syzygies 

(X 1 X 2 2 X 5 X 6 2 X 7 "X 9 X 10 ' i ) (X 1 X 3 X 4 "X S X 8 
= (X 1 2 X 3 X 5 X 6 2 X 7 X 8 2 X 10 3 






corresponding to the fundamental general magic squares 



46 MAJOR P. A. MACMAHON: MEMOIR ON THE 

2 1 
2 1 

1 2 



1 


2 





1 





2 








2 





1 





1 


2 


2 


1 














1 


2 


2 





1 





2 


1 








1 


2 

















1 


1 


1 




















1 


1 


1 




















1 


1 


1 









connected by the fundamental syzygies 

120 102 111 201 021 
012 + 210=2111= 012 + 210. 
201 021 111 120 102 

Art. 133. If the sum of each row, column, and diagonal be 3, the number of 
general magic squares of order 3 that can be constructed is, from the generating 
function, the coefficient of ar*" in the expansion of 

(l-.x- H )-(l-;r<)-'\ 
and this is found to be 

n 2 +(n+l) 2 . 

Art. 134. The ordinary magic squares, the component integers being 0, 1, 2, 3, 4, 
5, G, 7, 8, are eight in number and are easily found to be 

723 
=048, 
561 

and seven others obtained from 

120 201 120 021 120 021 

3012 + 012, 012+3210, 3012 + 210, 

201 120 201 102 201 102 

102 201 102 201 102 021 
210+3012, 3210 + 012, 210+3210, 
021 120 021 120 021 102 

021 021 
3210 + 210. 
102 102 

Art. 135. There is no theoretical difficulty in proceeding to investigate the squares 



120 
1 2 
2 1 


2 1 
+ 3012 
1 2 



THEORY OF THE PARTITIONS OF NUMBERS. 47 

of higher orders, but even in the case of order 4 there is practical difficulty in 
handling the H generating function. There are 20 fundamental squares, viz. : 



1 











1 














1 











1 














1 














1 








1 














1 











1 





1 








1 

















1 








1 














1 














1 


1 

















1 











1 














] 











1 


1 














1 








1 














1 











1 

















1 








1 





I 




















1 


1 














1 














1 





1 


1 








1 





1 








1 





1 








1 


1 


1 





1 











1 


1 


1 


1 











1 





1 





1 





1 


1 


1 














1 


1 


1 





1 











1 


1 





1 





1 


1 





1 





1 


1 











2 














2 





1 





1 





1 


1 








1 





1 








1 





I 











2 





1 


1 











1 


1 


1 


I 











1 


1 














2 


1 








1 


1 








1 


1 


1 








1 





1 





1 








1 


1 








1 








1 


1 





1 





I 


1 


1 














1 


1 





1 


1 





2 














1 





] 


1 





1 





2 














1 


1 











2 








2 











1 





1 








1 


1 



10. 

Art. 136. The direct enumeration of general magic squares of given order and sum 
of row. 

Let h w denote the sum of all the homogeneous products w together of the 

magnitudes 

a,, .,,..._!, . 

If h w be raised to the power n and developed, the coefficient of 



is the number of squares that can be formed of order n, so that the sum of each row 
and column is w, but in which there is no diagonal property in evidence."" 

* "Combinatorial Analysis The Foundations of a New Theory," 'Phil. Trans.,' A, vol. 194, 1900, 
p. 369 et seq. 



48 MAJOR P. A. MAcMAHON: MEMOIE ON THE 

In fact, if 

(x-a l )(x-a 3 )...(x-OL a ) = x"-p l X n - l +...+(-) a 

and 



w! D H , = 

an operator of order w obtained by raising the linear operator to the power w 
symbolically as in TAYLOK'S theorem, then the number in question is concisely 
expressed by the formula 

D'V, 

a particular case of a general formula given by the author (loc. cit.). 
Art. 137. To introduce the diagonal properties, proceed as follows: 
Let /;.,,. ( * ) denote what !>,, becomes when Xa s , /Aa,,_., +1 are written for a n _, + i 

respectively, and form the product hj-^ h w (2 \ . . h,^"\ 
1 say that the coefficient of 



in the development of this product is the number of general magic squares of order n 
corresponding to the sum w. 

To see how this is take 'n = 4, w = 1, and form a product 



x 
and observe that, in picking out the terms 



one factor must be taken every time from each row, column and diagonal ot the 
matrix. 

Similarly, if n = 2, we form the product 



x { X a a/ + X^a 2 a 3 + ^a z 2 + (Xa 2 + /ua 8 ) (a! + a 4 ) + a^ + ajOt 4 + a 4 2 } 
x X a a 2 +XAaa + l t 2 a 2 +Xa + xa) (a 1 + a 4 ) + a 1 :J + !< + a/} 



In forming the term involving 

xy % VV 

regard the successive products as corresponding to the successive rows of the square, 
the suffix of the a as denoting the column, and X, fi as corresponding to the 
diagonals. 

Thus picking out the factors 

XX 2 , /ua 3 a 4 , y* 2 a 4 , a 2 a 3) 



THEORY OF THE PARTITIONS OF NUMBERS. 49 

we obtain the corresponding square 

2000 

0011 
1 1 ' 
0110 

These examples are sufficient to establish the validity of the theorem. 
. Art. 138. If we wish to make any restriction in regard to the numbers that appear 
in the s ih row, we have merely to strike out certain terms from the function 

7, () 

n w . 

E.g., if no number is to exceed t, we have merely to strike out all terms involving 
exponents which exceed t. 

If the rows are to be drawn from certain specified partitions of w, we have merely 
to strike out from the functions 

h (1) h <2) h (n) 

"'HI ) n 'w 

all terms whose exponents do not involve these partitions. 

We have thus unlimited scope for particularising and specially defining the squares 
to be enumerated. 

Let us now consider the enumeration of the fundamental squares of order n, such 
that the sum of each row, column and diagonal is unity. Observe that if the 
diagonal properties are not essential the number is obviously n \ 

Art. 139. It is convenient to consider a more general problem and then to deduce 
what we require at the moment as a particular case. I propose to determine the 
number of squares of given order which have one unit in each row and in each column, 
and specified numbers of units in the two diagonals. 

Consider an even order 2n, and form the product 



X (a, + Xa 2 + a 3 + . . . 
x (a, + a 2 + Xa 3 + . . . 



- 2 + Xa 2)l _i + a 2n ) 
x (/*! + a 2 + 3 + . . . + a 2;i _ 2 + .,_! + Xa 2 ,,). 
We require the complete coefficient of 



when the multiplication has been performed. 
Writing Sa = 

VOL. CCV. A. H 



50 MAJOR P. A. MACMAHON: MEMOIR ON THE 

the product is, taking the th and 2n+l-t th factors together, 



-!) a 2 +(X-l) a 2B _i 



Observing that we only require terms which involve the quantities a with unit 
exponents, the product of the first two complementary factors is effectively 



and the complete product 



has, on development, the form 

s 2 " + A,* 2 "- 1 + A 2 .s- 2 "- 2 + . . . + A 2 ,,, 

where A,,, is a linear function of products of the quantities a, each term of which 
contains m different factors a, each with the exponent unity. 
Since, moreover, x"' gives rise to the term 

ml ^0.^2... a,,,, 

it follows that the coefficient of Sia 2 ...a a ,, in the product is obtained by putting each 
quantity a equal to unity and s m = m\. 

Hence, if S" = ml symbolically, the symbolic expression of the coefficient is 



or 



or writing 

-s 2 4.S + 2 = o- 2 , .s 1 = 



This is the complete solution of the problem for an even order 2n. 
For an uneven order 2+ 1, it is now evident that the symbolical expression of the 
coefficient of 



is 

{ o- 2 + 2 (X + /i) a, + X 2 + ^Y (o-i + V) 

the complete solution in respect of the uneven order 2n+l. 



THEORY OF THE PARTITIONS OF NUMBERS. 



51 



Art. 140. To find the number of ground "general magic squares" corresponding to 
the sum unity, we have merely to pick out the coefficient of X/u, ; we thus find 



even order 2n number is 8 ( ) a- a n ~ 3 <ri a , 

w 

uneven order 2n+l number is 8 (2) tr 2 n ~ 2 cr 1 3 +o- 2 ", 



wherein it must be remembered that the a- products are to be expanded in powers 
of s and then s m put equal to m I 

In the general results the coefficient of 

xy* 

gives the number of squares in which the row and column sums .are unity and the 
dexter and sinister diagonals' sums are I, m respectively. 
I give the following table of values of simple a- products : 



0-2 



9 


4 


4 


44 


24 


16 



r. 



_ 2_ 2 
CTj <T 2 



(TjOj 






265 


168 


116 


80 


1854 


1280 


920 


672 



The numbers cr/ = (s l) p denote the number of permutations of p letters in which 
each letter is displaced and constitute a well-known series. 

The remaining numbers are' readily calculated from these by the formula 

O-/G-/ = o-/ +2 o-/- 1 -2cr/ +1 o-/- 1 -<o-/- 1 . 

Art. 141. Another solution of the same problem yielding a more detailed result is 
now given. 

For the even order 2n I directly determine the coefficient of 



in the product above set forth. 



H 2 



52 MAJOE P. A. MACMAHON: MEMOIR ON THE 

We have to pick out I X's and m /i's and to find the associated factors, 2n-l-m in 
number, which are linear functions of the quantities a. 

In any such selection of I X's and m /u's there will be i pairs of X's symmetrical 
about the sinister diagonals and./ pairs of>'s symmetrical about the dexter diagonals, 
and the associated factors will depend upon the numerical values of i and j. 

Consider then in the first place the number of ways of selecting I X's in such wise 
that i pairs are symmetrical about the sinister diagonals. 

This number is readily found to be 



n w 

i l-2i 



With these I X's we cannot associate any /u which is either in the same row or in 
the same column as one of the selected X's. 

Each of the i symmetrical pairs of X's in this way accounts for 2 /A'S, and each of 
the l2i remaining X's accounts for 2 p's. 

Thus we must select m p's out of 2n-2i-2 (l2i) p-'s, i.e., m /A'S out of 
2n-2l + 2i fi's. 

We may select these so as to involve / pairs symmetrical about the dexter 

diagonals in 

(n-l+i\/n-l+i-j\ ,j 

\ j !\ m2j I 

This number is obtained by writing in the first formula nl + i,j and m for 

n, i and I respectively, 

and observe that we may do this because the selection of a symmetrical pair of X's or 
of one of the remaining X's results in the rejection of a pair of /x's which is 
symmetrical about the dexter diagonals. 

Consequently the 2n2l + 2i possible places for the m /A'S are also symmetrically 
arranged about the dexter diagonal. Hence the formula is valid. 

We have established at this point that we may pick out I X's involving i 
symmetrical pairs and m /LI'S involving j symmetrical pairs in 



. 
\ij\l-2ij \ J J\ m-2j j * 

We must now determine the nature of the 2n I m associated factors, linear 
functions, of the quantities a. 

In the matrix of the product delete the rows and columns which contain selected 
X's and /A'S. We thus delete l + m rows and l + m columns. 

Consider the 2nlm remaining rows. There remain in these rows at most 

2n I m 
elements a, because l + m columns have been deleted, but some of these elements 



THEORY OF THE PARTITIONS OF NUMBERS. 53 

must be rejected if they involve X or p. as coefficients, because by hypothesis we are 
only concerned with I X's and m //.'s, and these have already been accounted for. 

Observe now that the columns which contain a symmetrical selected pair of X's 
only contain /t's which are in the same rows as these X's, and therefore the deletion of 
these columns cannot delete p.'s appertaining to any rows except those occupied by 
the selected pair of X's. Observe further that the column which contains an 
unsymmetrical X, say in the p ih row, contains a /A in the 2np+I a> row, and that 
therefore the disappearance of a p. in the 2n p+l th row follows from the deletion of 
a column containing an unsymmetrical X in the p th row. 

Hence of the 2n I m rows in question 

l + m %i 2j rows contain '2nlml, a elements, 
and thence 

2n 2l 2m+2i+2j rows contain '2iilm2, a. elements. 

Accordingly if s is the sum of all the a elements except those which appear as 
coefficients of the selected X's and /A'S the co- factor of 

n\ in-i\ 9 ,- 2i in-l 



l-2i 
contains l + m2i2j factors of type 



and 2n 2l 2m + 2i + 2j factors of type 

(*--,,), 
or ofnlm + i+j squared factors of type 

(s-oi v -.)*, 

since these factors occur in equal pairs. 

Hence the co-factor is 

n(*-a,,)ll(.s-a,.-a,,.) 2 , 

wherein the quantities a u , l + m2i2j in number, which appear in the first product, 
and the quantities ., 2n2l-2m + 2i+2j in number, which appear in the second 
product, are all different. 

Also (s <* a K ,) 2 is effectively equal to 

s 2 2 ( + a,,.) s + 2a v a. u , 

since squares of the a's may be rejected. 

Hence, by the reasoning employed in the first solution we may put the quantities 
a equal to unity, regard s p as equal to p ! symbolically, and say that the coefficient of 

in the product 



54 MAJOE P. A. MACMAHON: MEMOIR ON THE 

has the symbolical expression 



or, putting 

sl = o-j, s*-4s + 2 = o- 2 , 

we obtain 

/n\ ni - _ 



for the number of squares such that 

(1) Sum associated with rows and columns is unity ; 

(2) There are I units involving i symmetrical pairs in the dexter diagonal ; 

(3) There are m units involving j symmetrical pairs in the sinister diagonal. 

Giving i and j all possible values we find that the complete coefficient of 



in the product, which we have already ascertained to have the expression 



may be also expressed in the form 

n ~ l H ~ 



fn-l+ 1 
\ m 



THEOKY OF THE PARTITIONS OF NUMBERS. 



55 



Further simplification of this series cannot he effected because each term of the 
sum must be considered on its merits and does or does not add to the numerical 
result as may appear. 

Art. 142. Writing the result for even order 2n 



it appears that the result for uneven order 2i+l may be written 



For the squares of simple orders we have the results 
ORDER 2. 



1 2 








1 














1 






1 = 



1 

2 
3 


ORDER 3. 
0123 





2 








2 








1 

















1 









ORDER 4. 



1= 1 



4 





8 


4 





1 











4 





2 























1 















Z= 




ORDER 5. 

12345 



II 

s 



16 


16 


8 


4 








16 


20 


4 


4 





1 


8 


4 


8 











4 


4 





2 





























1 















56 



MAJOK P. A. MACMAHON: MEMOIK ON THE 

ORDER 6. 
1= 1 2 3 4 5 6 







80 


96 


60 


16 


12 





1 


96 


96 


48 


24 











60 


48 


24 





3 








16 


24 

















12 





3 



































1 


















Art. 143. I now proceed to consider the enumeration of the squares of even 
order 2n, such that every row and column contains two units, and the dexter and 
sinister diagonals / and m units respectively. 

I form the product 



n 

CC-2 



< 2 > 



where 2 <s) is the sum two together of the quantities 



and I seek the coefficient, a function of X and /x, of 

(ajOa^.o^) 8 

in the product. 

The coefficient of X'/u, in the sought function of X and p. is the required number. 
Let pi, p 2 he the sum and the sum two together of the quantities 



then 



whence 



+ 2 (Xyx-1) 



+ terms involving powers of 1; 2;1 above the second. 



THEORY OF THE PARTITIONS OF NUMBERS. 57 

The product of a 2 (l \ 2 (2 ' is thus, after re-arrangement, effectively equivalent to 
pf+ (A + /A-2) (a, + 03.) #tf>,- (X + /4-2) (a^ + ag. 8 ) p. 



4)}a 1 a 8( (a, +*,)/,, 

2! 2 . 
Regarded apart from > 2 , ^ this expression is a function of a,, a 3 , ; the product 

a^a/- 1 ' 
is a function of 2 , a 2 -i> and generally the product 



is a function of at,, a a ,, +1 _ s , and all of these products are of similar form in regard to 

Pa, Pi, ^, P- 

Remembering that we desire the coefficients of 

(!,... a 2 ,) 2 
in the product 



we must distinguish between p 2 where it occurs as a multiplier of af' + a^ and where 
it occurs as a multiplier of a^a,,, and make a similar distinction in respect of ^, 2 . 
Put then 



(tti' + as,, 2 ) pi 2 = (ai 2 + a ,, 2 ) H^. 
Putting further the quantities a equal to unity and regarding a product 

PaP\irfir^ 
as a symbol for the coefficient of symmetric function 

/0+rfli + -'-\ 

in the development of symmetric function 

(i 2 )- + "(ir 2 ', 

I say that 

> 1 -2 (X +j u-2)^ 3 + 2 (X-l) (/*- 



is the symbolic expression of the required coefficient of 



VOL. CCV. - A. 



58 MAJOR P. A. MACMAHON: MEMOIR ON THE 

This may be written 

{o- 4 + 2 (X + /*) 03+(X 2 + /t s ) <r,+ 2\po f a +2\p. (X + /t) 0-, + XV 2 }", 
0-4 = pa-^paPi + 4 (p + j) + 2 (pj 2 + 7T, 2 ) - 8p, + 3, 

0-3 = ^2^1 - ( P2 + 7I- 2 ) - ( p^ + TTj 2 ) + 5pi - 2, 

o- 2 =j>! 2 - 4^ + 2, 



where 



For the uneven order 2>i + l it is easy to show that the coefficient is symbolically 

2X^ (X + ya) o-^XV}" x ( ^- 
It is easy to calculate the values of 

KpiVV 

for small values of <t, />, c, d. 

Some results are, omitting the obvious result 2^1 b ', 



a. 


b. 





d. 


Value. 


1 















1 




1 








l 


1 




1 


1 




3 




1 




1 


3 


1 




1 




2 


1 






1 


2 




2 


1 




12 


1 


2 






5 






2 




6 








2 


6 






1 


1 


5 



THEORY OF THE PARTITIONS OF NUMBERS. 59 

enabling the verification of the results 

o- 4 = cr :j = o- 2 = rr' 2 = <r, = 0, 
o-/ = 4, <r s o-, = 0, o-V = 2. 

Hence for the even order 2 the whole coefficient is X 2 /n a , corresponding to the only 
possible square 



1 


1 


1 


1 



and I find for the uneven order 3 



Art. 144. To find in general the number of squares which have two units iu each 
diagonal we find the coefficient of X 2 ja 2 and obtain for even order 2n. 



<r 4 - 4 96er, 4 ; 



putting n = 2 we find for the order 4 

2o-4 + 2cr/ + 4cr'/+l 60-30-1 

and the verification of this number is easy. 

For the uneven order 2n+l we obtain the number 



'tr/^ 2<r> 1+ (gJcrr^ 



^ (<r 3 a o- 3 + 2o- 3 V 8 ) + ' 

- 



The general value of 



may be obtained by means of the calculus of finite differences. 

There is no theoretical difficulty in finding symbolical expressions for the enumera- 
tion of general magic squares associated with higher numbers, but the method does 
not lead to the determination of general magic squares. These must be regarded as 
arising from the generating function method of 9. 



I 2 



III. Atmospheric Electricity in High Latitude.^. 

By GEORGE C. SIMPSON, H.Sc. (18Z1 Exhibition, Scholar of tic I'niverxity 

of Manclicxter). 

Communicated by ARTHUR SCHUSTKI;, F.ft.S. 
Received February 17, Read March -2, 190;"). 

INVESTIGATION into the problems of atmospheric electricity may be divided into two 
periods. The first period was devoted almost entirely to measurements of the 
normal potential gradient in the lower region of the earth's atmosphere, with the 
aim of finding its daily and yearly variations, its geographical distribution and its 
dependence on meteorological condition. To this period belongs the fine work of 
Lord KELVIN and Professor EXNEE.* 

The second period commenced in 1899, when the interest in the problems of 
atmospheric electricity was at rather a low ebb, owing to the small real progress 
made during the latter few years. In that year the discovery that atmospheric air 
is always more or less ionized made at about the same time by ELSTKR and 
GEiTEt,t in Germany and C. T. R. WlLSONj in England had a completely revo- 
lutionizing influence on the theories held to account for the earth's normal field. 
This discovery has brought about a great revival of interest and opened a totally 
new field for investigation. 

As long as air could be considered a perfect non-conductor EXXEK'S theory that 
the charge on the earth is a residual charge held a very strong position ; but with a 
conducting atmosphere it is untenable. An ionized atmosphere means a continual 
passage of electricity from the charged surface into the highest regions of the atmo- 
sphere, where only any residual charge could be held. The new discovery having 
proved conclusively that the charge on the earth is being continuously dissipated 
into the ionized air above, it became of prime importance to determine the rate 
at which the electricity is dissipated and the conditions under which the loss 
takes place. 

The first serious attempt to do this was made by ELSTER and GEITEL. They 
designed an instrument consisting of a charged cylinder exposed to the air 

* For a good resumf of this period see EXNER, ' Terr. Mag.,' vol. 5, p. 167, 1900. 
t 'Phys. Zeit.,' 1, p. 245, 1899; 'Phys. Zeit.,' 2, p. 116, 1900. 
\ <-Roy. Soc. Proc.,' 68, p. 151, 1901. 

'Phys. Zeit.,' 1, p. 11, 1899; 'Terr. Mag. and Atm. Elect.,' 4, p. 213, 1899; ' DRUDE'S Aim.,' 2, 
p. 425, 1900. 

VOL. COV. A 389. 28.7.05 



62 MR. GEORGE C. SIMPSON ON THE 

protected from extraneous electrical fields and so connected to an electroscope that 
the rate at which it lost its charge could be measured. By making certain assumptions 
it can be shown that the charge lost in a small interval of time from any charged 
body exposed to the air is always a definite fraction of the charge on the body. 
Thus, when ELSTER and GEITEL had found the charge lost by their cylinder in a 
minute, they were able to express the loss as a percentage of the charge on the 
cylinder, and then, by applying this percentage to the charge on the earth, were able 
to find the quantity of electricity being dissipated from every square metre of surface 
each minute. 

Besides knowing the amount of electricity dissipated from the surface which 
depends upon many factors it became also of great importance to know to what 
extent the air is ionized at any moment. For this purpose EBEKT* designed an 
instrument which gives the amount of ionization independently of everything else. 
A known quantity of air is drawn through a cylinder condenser, the inner cylinder ol 
which is connected to an electroscope. As the air passes between the cylinders 
the charged inner one attracts t< it all the ions of the opposite sign. These ions 
neutralize an equal amount of electricity, and so the charge lost by the inner cylinder 
is a measure of the number of ions contained in the known quantity of air which has 
been drawn through the instrument. In this way it is possible to find how many 
electrostatic units of each kind of electricity are free in a cubic metre of air. 

These two instruments are very powerful weapons for attacking the new problems 
of atmospheric electricity, and have been used as such to a large extent on the 
Continent. Systematic observations of the dissipation were undertaken by ELSTER 
and GEITEL, and quite a number of other physicists have devoted themselves to 
finding the relations existing between meteorological conditions, ionization, the rate 
of dissipation and the potential gradient. As a result of this work the electrical 
conditions of the atmosphere are already fairly well known for lands lying within the 
temperate zone. With the idea of extending this knowledge to places within the 
Arctic Circle I was granted permission by the Commissioners of the 1851 Exhibition 
Scholarship to undertake a year's work on atmospheric electricity in Lapland. 
The work which I proposed to do was the following : 

1. By means of a Benndorf self-registering electrometer to obtain daily curves 

of the potential gradient and from these to calculate the yearly and 
daily variation. 

2. To make systematic observations of the dissipation by means of ELSTER 

and GEITEL'S instrument. 

3. To make corresponding measurements of the ionization with EBERT'S 

apparatus. 

* Short description, ' Phys. Zeit.,' 2, p. 662, 1901; fuller description, ' Aeronautische Mittheilungen ' 
p. 1, 1902. 



ATMOSPHEKIC ELECTRICITY IN HIH LATITUDES. 63 

4. To measure the amount of radio-active emanation in the atmosphere. 

5. To investigate as far as possible the influence of the Aurora on the 

electrical conditions of the atmosphere. 

In my choice of a station I decided to get as far north as possible without being 
actually on the sea coast, and found that the Lapp village of Karasjok (69 17' N., 
25 35' E., 129 metres above sea-level) was very wfll suited for my purpose. 

Meteorological Conditions. 

Before going on to a discussion of the electrical results obtained, it will be as well 
to give a short account of the meteorological conditions experienced during the year's 
work. From its high latitude the north of Norway should be a very cold district ; 
but the presence of the open ocean on the north and West greatly modifies the 
temperature. The effect of the water is of course very much more marked on the 
sea coast than inland. As one recedes from the coast the mean temperature for the 
winter six months falls very rapidly, it being 2'3 C. at Gjesvoer, near the North 
Cape, and 11'7 at Karasjok. If there were no interchange of air between the ocean 
and the interior of the land the latter would of course have a very low temperature. 
This became very noticeable during periods of calm weather, for the temperature 
would then run down to very low values, reaching on several occasions 40 ('., 
while, on the contrary, whenever the wind rose the temperature rose also. 

When there was no wind, a cap of very cold air would form over the land, causing a 
nearly permanent temperature inversion. Although 1 could not observe this inversion 
instrumentally neither kites nor balloons forming part of my equipment there could 
be little doubt as to its reality. On September 3()th, with an air-temperature of 
G C., a bright rainbow was observed. Then again, on descending the high banks 
of the river, one felt at once the cold air collected in the river basin, and the Lapps 
stated that it was seldom as cold on the hills as in the valleys. Then, again, the fact 
that a wind was always accompanied by mild weather also points to the cold of still 
weather being confined to a laver of air of no considerable depth lying over the surface. 
This condition of things almost entirely prevented the formation of ascending currents 
of air, so causing very small values of the amount of precipitation and almost entirely 
preventing the formation of low clouds during the winter. It also had a very marked 
effect on the electrical condition of the atmosphere, to which reference will be made 
later. 

During the summer the weather conditions were very similar to those of England, 
with the exception that the precipitation was very much less and thunderstorms were 
scarce. On three days only was thunder heard and lightning was not seen once. 

From November 26 to January 18 the sun did not rise above the horizon; never- 
theless, even in the darkest days there were two or three hours of twilight during 
which the sky was too bright for the stars to be seen. The period during which the 
sun did not go below the horizon extended from May 20 to July 22. 



64 MK. GEORGE C. SIMPSON ON THE 

Methods of Work* 

Potential Gradient. BENNDORF'S self-registering electrometer, with radium collector 
attached, was set in action on September 28, 1903, and produced a nearly continuous 
record of the potential gradient until October 1, 1904. Each day the curve for the 
previous day was measured and the mean potential gradient for each hour obtained. 
Tli is was done by first drawing a curve as smoothly as possible through the registered 
curve, then five equidistant ordinates in each hour were measured, and the mean of 
these five taken to represent the mean potential gradient during the hour. In 
discussing the potential gradient for any place it is usual to use only observations 
made during fine weather, neglecting all those which have been affected by any 
atmospheric disturbance. This plan I also followed during the summer months (April 
to end of September), for then the curves drawn by the instrument were exceedingly 
regular unless there was actually precipitation taking place in the neighbourhood. 
But during the winter the curves were so irregular, even on the finest days, that it 
was quite impossible to decide whether a particular curve ought to be neglected or 
not, so T used, during the winter, all the curves quite independently of the weather 
This caused irregularities in the final curves, but has not, I think, affected the 

cl 

conclusion to be drawn from them. 

Iti^iitxtioii. The value of the dissipation, as measured by ELSTER and GEITKL'S 
instrument, depends to a very great extent on the manner in which the instrument 
is exposed to the wind. This is as it should be, for the actual dissipation from the 
earth's surface (which the instrument is designed to measure) depends largely on the 
\vind strength. In order that the instrument should measure the amount of dissipation 
taking place from the earth's surface, it should be exposed to the same wind condition 
as the general surface. This fact has not been fully realized by most observers. It 
has been quite a common practice to shelter the instrument from the wind, either by 
erecting screens or by observing close to a building, and in several cases the instrument 
has been placed within a room close to an open window. Observations taken under 
such conditions are of very little value : they are certainly of no use in comparing the 
dissipation of one place with that of another, and at the best can only be used to 
compare variations from time to time at the same place. In order that the dissipation 
at one place may be compared with that of another, the instruments used should in 
both cases be exposed to the full force of the wind, for wind strength is just as much 
a factor in determining the dissipation as is the ionizatiou. For this reason my 
instrument was only used in a freely exposed situation, where it was in no way 
sheltered from the wind. This method also has its drawbacks, for with anything like 
a high wind the leaves of the electroscope were so blown about that they continually 
discharged the instrument by coming in contact with the case. Hence measurements 
could not be made in very high winds, and so the mean values of the dissipation 

* For fuller particulars of methods of work and arrangement of apparatus see Appendix. 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 



found are slightly less than they would have been if observation could have been 
made in all winds ; but the final results are very little affected. Observations also 
could not be made during rain, owing to trouble with the insulation. Except when 
it was impossible to observe, owing to these two causes, measurements of the 
dissipation were made three times each day, between 7.30 and 9.30 in the morning, 
between 12 and 2 midday, and between 6 and 8 in the evening. 

In expressing the dissipation, ELSTER and GEITEL'S example has been followed, 
i.e., the dissipation is expressed as the percentage of charge lost by a charged body in 
a minute. Thus a+ = TOO per cent, means that 1 per cent, of the positive charge on 
any body will be dissipated in a minute ; similarly, a_ expresses the dissipation of a 
negative charge. The ratio a_/a+ is written q. There are two methods of obtaining 

the mean value of this ratio, either - 2 ( ) or - ; in most cases these two are very 

n \a+/ Sa+ 

nearly equal. In this paper q is always obtained by the latter method. 

lonization. EBERT'S instrument for measuring the ionization was used at the same 
time as the dissipation instrument. It was often possible, however, to use the Ebert 
apparatus on days when the wind made -it impossible to use the dissipation apparatus ; 
but, on the other hand, the insulation of the Ebert instrument would often fail, owing 
to high humidity of the atmosphere, when satisfactory measurements of the dissipation 
could be obtained. EBERT'S instrument also could not be used when the temperature 
fell below 20 C., for then the oil in the air turbine froze and prevented the clock- 
work running freely. EBERT'S method of expressing the ionization has been followed ; 
the positive ionization is expressed as the number of electrostatic units of free 
positive ions in a cubic metre of air ; similarly for negative ionization. The symbols 
used to denote positive and negative ionization are 1+ and I_ respectively. The ratio 
of positive ionization to negative, i.e., I+/I-, is written r, and the mean is obtained by 
the process 2I+/SI-. 

RESULTS OF THE OBSERVATIONS. 

Yearly Variations. 

Potential Gradient. Table I. gives the monthly values of the potential gradient. 

TABLE I. Potential Gradient. 



Winter. 


Volts/metre. 


Summer. 


Volts/metre. 


October . 


121 


April 


131 


November 


167 


May 


103 


December 


175 


June 


90 




199 


July 


98 




209 




93 


March 


191 


September .... 


93 











VOL. CCV. A. 



fiB MR. GEORGE C. SIMPSON ON THE 

The yearly course of the potential gradient is shown in Curve I., fig. 1, on which 
each point gives the mean potential gradient for a week, the means for the months (as 
in Table I.) being shown by points enclosed within circles. It will at once be seen how 
irregular the potential gradient is during the winter when taken for such short time 
intervals as a week ; on the contrary the monthly means fall very nearly on a regular 
curve. It must be remembered that, as stated above, these values during the winter 
are obtained from both fine and disturbed days. If only fine days had been used not 
only would the curve have been more regular, but also the mean potential gradient 
would have been greater. The trend of the curve may be summed up as a regular 
rise in the potential gradient from. October to the middle of February, followed 
by a more rapid fall until the end of May, after which the potential gradient remains 
nearly constant during the summer months. 

Dissipation. The mean values of the dissipation for each month are shown in the 
following table. In order to find the effect of the seasons, and whether the total 
absence of the sun for nearly three months during the winter and its presence for an 
equal length of time during the summer influences the electrical conditions of the 
atmosphere, the observations have been grouped into periods of three months, the 
winter three months containing the period of no sun and the summer three months 
that of permanent sun. 



TABLE II. Dissipation. 



Months. 


a + . 


a_. q. 


a . 


Seasons. 


+. 


_. 


? 


a . 


November 


3-20 


3-43 1-07 


3-32 


1 










December 


2-13 


2-53 1-19 


2-33 


} Winter . 


2-44 


2-76 


1-13 


2-61 


January 


1-98 


2-33 1-18 


2-17 


J 










February 


1-37 


1-47 1-08 


1-42 


} 










March 


2-79 


3-74 1-34 


3-27 


> Spring . 


2-65 


3 '20 


1-20 


2-92 


April. 


3-78 


4-38 1-16 


4-07 


J 










May. 


4-41 


4-76 1-08 


4-58 












June. 


4-24 


4-68 1-10 


4-45 


Summer . 


4-63 


5-14 


1-11 


4-88 


July . 


5-25 


5-97 1-13 


5-61 












August 


4-32 


4-94 1-14 


4-63 


] 










September 


4-28 


4-89 1-14 


4-58 


> Autumn . 


3-60 


4-16 


1-15 


3-88 


October . 


2-21 


2-65 1-20 


2-43 


J 


















Whole year 


3-33 


3-82 


1-15 


3-57 



On Curve II. these values of the dissipation (a ) have been plotted, also the 
weekly values. If no observations were made for a week a gap has been left in the 
curve. From the curve it will be seen that the yearly course of the dissipation is 
strikingly similar to that of the potential gradient when inverted, the one falling and 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 



67 



IDECEMSERI JANUARY 



I FEBRUARY | MARCH | APRIL | MAY | JUNE | JULY | AUGUST 



APRIL I MAY JUNE I JULY I AUGUST [SEPTEMBER 



NOVEMBER IDECEMBER [JANUARY I FEBRUARY I MARCH 




68 



ME. GEORGE C. SIMPSON ON THE 



rising at exactly the same time as the other rises and falls, and both remaining 
constant during the summer. These curves suggest that there is some relation 
between the two phenomena ; this relation will be discussed later in the paper. 

The ratio of the negative dissipation to the positive (q) does not appear from these 
results to have a regular yearly course, but when they are considered in connection 
with the ionization it will be seen that it is very likely there is a yearly variation 
with a maximum in the winter and a minimum in the summer. 

Ionization. Table III. gives the monthly mean values of the ionization. 

TABLE III. Ionization. 



Months. 


I_. 


I+. 


T. 


I - 


Seasons. 


I_. 


I + - 


r. 


I. 


November 
December 


25 
28 


35 
39 


1-40 
1-39 


30 
33 


^ Winter . 


26 


33 


1-28 


29 


January . 


25 


26 


1-04 


25 


J 










February 
March . 


20 

28 


24 
32 


1-20 
1-14 


21 
30 


I Spring . 


26 


31 


1-19 


28 


April 


31 


38 


1-22 


34 


J 










May . 


35 


40 


1-18 


37 


1 










June . 


37 


41 


1-09 


39 


> Summer . 


38 


42 


1-11 


40 


July . . 


42 


46 


1-10 


44 


J 










August . 
September 
October . 


45 
42 
34 


51 
46 
40 


1-13 

1-08 
1-18 


48 
44 
36 


> Autumn . 


40 


46 


1-15 


43 












Whole year 


33 


38 


1-17 


36 























These results, together with the weekly means, have been plotted in Curve III. 
Here we have quite a different curve from either of the two previous ones. Instead 
of the rapid fall and rise in the winter followed by a constant period during the 
summer we have a six months' linear fall from August to February followed by a 
similar six months' linear rise from February to August. 

That there should be such a great difference between the curves for the dissipation 
and the ionization was not to be expected, and at first one would be inclined to doubt 
the correctness of one or other of them. But this can be tested by the following 
considerations. The dissipation depends practically only on two factors : ionization 
and wind strength. If the effect of the latter could be eliminated, the course of the 
dissipation should then be the same as that of the ionization. In order to see if this 
were so, I took all my measurements of the dissipation and separated them according 
to the strength of the wind as estimated at the time of observation, then, using only 
one definite wind strength, took the means for each month and plotted them. ' The 
result is shown in fig. 2. Each curve represents one wind strength, and it will at once 



ATMOSPHEEIC ELECTEICITY IN HIGH LATITUDES. 69 

be seen that all four curves are practically parallel* and are similar in shape to that of 
the ionization. This shows at once that both the curves of the dissipation and 
ionization are correct, and that there is a real difference in the yearly course of 
the two, and also that there is a closer relation between potential gradient and 
dissipation than between potential gradient and ionization. 



APRIL I MAY | JUNE | JULY | AUGUST [SEPTEMBER 



OCTOBER | NOVEMBERIDECEMKRlJANUARY [FEBRUARY] 




Fig. 2. 

The value of the ratio !+/!_ shows a very distinct yearly period with a maximum 
in the winter and a minimum during the summer. Later it will be seen that very 
probably this ratio depends largely on the potential gradient, so that its yearly 
period might be expected on account of the yearly variations in the potential 
gradient. 

Daily Variations. 

Potential Gradient. The daily course of the potential gradient varies greatly 
according to the season of the year. For this reason five curves of the daily course 

* The lowness of the two curves for wind strengths 0-1 and 1-2 during the first part of the winter is 
due to the fact that, owing to the darkness at both the morning and evening observations then, it was 
impossible to see if the smoke of the village was drifting towards my place of observation or not. Nor 
was I quite aware then of the fact, which I found later, that with no wind the smoke of the village 
extended in an almost invisible haze over the whole valley, out of which it could not get. This smoke 
effect, of course, only acted when there was insufficient wind to drive the smoke away, and its effect is 
not at all visible on the two curves with wind strength greater than two, i.e., a steady breeze. 



70 



MR. GEORGE C. SIMPSON ON THE 



are given : one each for the winter, spring, summer, and autumn three months and 
another for the year taken as a whole (fig. 3). It will at once be seen that the two 




A.M. 



11 12 1 
MID-DAY. 

Fig. 3. 



10 11 12 



curves for the winter and spring lie entirely above the curve for the year and those 
for the autumn and summer entirely below. 
The equations to the five curves are* : 

Winter three months, P = 180 + 64 sin (0+189) + 26 sin (20+155) + 4 sin (30+200), 
Spring P = 177 + 57 sin (0+176) + 37 sin (20+ 151) + 13 sin (30+ 195), 

Summer P = 97 + 16 sin (0+141)+ 9 sin (2(9+144)+ 4 sin (3(9+ 126), 

Autumn P = 103 + 23 sin (0+170)+19 sin (20+184)+ 2 sin (30+131), 

Whole year . . . . P = 139 + 39 sin (0+177) + 23 sin (20+158)+ 5 sin (30+178). 

From these equations we see that there are two periods which must be taken into 
account ; the amplitude of the third period falls without the limits of the accuracy of 
the instrument. Of these, the greater is a whole-day period and the lesser a half- 
day period. We also see that the phase of the main period undergoes a regular shift 
from a maximum in the winter to a minimum in the summer, which means that the 
evening maximum is earlier in the winter than the summer, thus following the sun. 
The phase of the second period does not vary regularly, and on account of its 

* These equations are worked out to mean local time, taking 12 o'clock midnight as the zero and 15 to 
represent an hour. All other time used in this paper is mid-European, which is 42 minutes behind mean 
local time. 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 



71 



smallness during the Bummer and autumn its position is not then well fixed. The 
ratio of the amplitude of the second period to the first is : winter '40, spring - 65, 
summer '56, autumn '83, whole year '59. This shows no regular variation ; the large 
value for the autumn is due to the strengthening of the second period by the 
formation of mists over the river about the times of sunrise and sunset, which mists 
always give rise to high potential gradients. 

The hourly values of the potential gradient corresponding to the five curves are 
given in the following table : 



TABLE IV. Daily Course of the Potential Gradient. 







12tol. 


1-2. 


2-3. 


3-4. 4-5. 


5-6. 


6-7. 


7-8. 


8-9. 9-10. 


10-11. 


11-12. 


Winter j 


A.M. 

P.M. 


138 
210 


119 103 100 
212 214 208 


90 
216 


Ill 141 
236 < 245 


148 
242 


162 187 
247 226 


184 
206 


214 

174 


Spring 1 


A.M. 

P.M. 


134 
193 


i 
122 : 107 
201 i 190 


99 
196 


99 
177 


109 
198 


135 

238 


146 
262 


164 175 
260 247 


187 
233 


187 
185 












































I 






Summer i 


A.M. 
P.M. 


101 
91 


93 

94 


86 
97 


81 
96 


77 
103 


81 86 
101 107 


90 
110 


90 90 
121 ! 131 


89 
122 


87 
108 


Autumn < 


A.M. 
P.M. 


87 
94 


75 
99 


70 
105 


70 
108 


72 
114 


78 90 102 
125 , 132 144 


108 106 
143 138 


93 
115 


90 
99 


Whole f 


A.M. 


115 


102 


92 : 87 ! 84 


95 113 j 121 


131 140 


138 


144 


year \ 


P.M. 


147 


151 


151 152 153 


165 


180 189 


194 185 


169 


142 










1 









Dissipation. As I had no self- registering instrument to record the dissipation and 
ionization, it is impossible to work out the daily course of these two as has been done 
for the potential gradient. Nevertheless, some idea of the course can be obtained by 
comparing the results according to the different times of observing. In Table V. the 
mean results from the morning, midday and evening observations are shown for each 
three months and then for the whole year. 



MR. GEORGE C. SIMPSON ON THE 



TABLE V. Dissipation. 





Morning (8 to 9 A.M.). 


Midday (12 to 1 P.M.). 


Evening (6 to 7 P.M.). 


a + . 


a_. 


<! 


a + . 


a_. 


? 


a + . 


o_. 


2- 


Winter. "| 
Three months, 1 
November, 
December, 
January J 


2-11 


2-71 


1-02 


2-02 


2-47 


1-23 


1-92 


2-37 


1-23 


Spring. 1 
Three months, I 
February, | 
March, April J 


3-00 


3-58 


1-19 


2-84 


3-29 


1-16 


2-08 


2-55 


1-23 


Summer. ~| 
Three months, I 
May, f 
June, July J 


4-54 


4-97 


1-10 


4-96 


5 31 


1-07 


4-45 


5-07 


1-14 


Autumn. 1 
Three months, | 
August, \ 
September, 
October J 


3-51 


4 '04 


1-15 


4-34 


4-85 


1-12 


2-92 


3-57 


1-22 


Whole year. . 


3-43 


3-83 


1-12 


3-54 


3-98 


1-12 


2-84 3-39 


1-20 



During the winter and spring the morning observations show a slightly higher 
dissipation than the midday, while, on the contrary, during the summer and autumn 
the midday values are the higher. For the whole year the dissipation is slightly 
higher at midday than earlier in the morning, while the evening observations show 
the lowest dissipation of the three. The value of the ratio q for nine months shows 
a daily period, being lower at midday than at either the morning or evening 
observations. The difficulties of observing during the winter three months make the 
value of the ratio found then very doubtful. 

The evening fall in the dissipation no doubt stands in some relation to the evening 
maximum of the potential gradient, while it is almost certain that the high evening 
value of q is directly caused by the high value of the potential gradient at that 
time. 

lonization. The results of the ionization observations are shown in Table VI. in 
the same way as those of the dissipation were in Table V. 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 
TABLE VI. lonization. 



73 





Morning (8 to 9 A.M.). 


Midday (12 to 1 P.M.). 


Evening (6 to 7 P.M.) 




I_. 


I + . 


r. 


I_. 


I + . 


r. 


I_. 


I*. 


r. 


Winter. ") 




















Three months, 




















November, \- 


27 


32 


1-20 


26 


35 


1-35 


24 


32 


1-35 


December, 




















January J 




















Spring. 1 




















Three months, 1 
February, [ 


27 


34 


1-26 


28 


31 


I'll 


23 


30 


1-30 


March, April J 




















Summer. "| 




















Three months, 1 
May, f 


39 


42 


1-08 


36 


43 


1-20 


36 


41 


1-14 


June, July J 




















Autumn. 1 




















Three months, 


















August, 


42 


46 


1-11 


41 


46 


1-13 


36 -44 


1-23 


September, 
October J 


















Whole year. . 


34 


39 


1-15 


33 -39 


1-18 


30 -37 


1-23 



The daily period of the ionizatiou is not so pronounced as that of the dissipation, 
but the ionization is slightly lower in the evening than in the morning or at midday 
during the whole year. There is practically no difference between the midday and 
morning ionizations. The daily period of the ratio q is a steady rise from the morning 
to the evening ; in this respect the ionization does not correspond with the 
dissipation. 

Interrelation of the lonization, Dissipation and Potential Gradient. 

Potential Gradient and Dissipation. The relation between potential gradient and 
dissipation has been very closely studied by GOCKEL* and ZOLSS. t The latter shows 
that the potential gradient varies very considerably with the dissipation, high 
potential gradient being accompanied by low values of the dissipation, and vice versa; 
and both show very clearly that the ratio of negative dissipation to positive 
dissipation rises considerably as the potential gradient rises. Table VII. shows the 



* 'Phys. Zeit.,'4, p. 871, 1903. 
t 'Phys. Zeit.,'5, p. 106, 1904. 



VOL. OCV. A. 



74 



MR. GEORGE C. SIMPSON ON THE 



results of my observations of the dissipation tabulated according to the potential 

gradient. 

TABLE VII Potential Gradient and Dissipation. 






Potential 
gradient. 


Winter. 


Summer. 


Year. 


a+. 


a_. 


2- 


a+. 


a_. 


2- 


a + . 


a_. 


f- 


volts/metre. 

50 to 100 
100 150 
150 200 
200 300 
300 400 
>400 


3-94( 5 ')* 
2-34( 03 ) 
l-75() 
1 32 () 
60( 12 ) 
51 H 


4-14(60) 

2-77 ( 64 ) 
2 43 ( 24 ) 
l-54( 41 ) 

S5( 13 ) 
64(20) 


1-05 
1-18 
1-39 
1-17 
1-42 
1-25 


4-50( 93 ) 
4-18( 81 ) 
2-50 (!) 
1-82 ( 5 ) 


5-02 ( 93 ) 
4-83 ( 8 ) 
3-47 O 
1-92 ( 5 ) 


I'll 
1-16 

1-38 
1-05 


4-29 ( 15 ) 
3-38O 
1-85 ( 26 ) 
1-37 ( 46 ) 
60 ( 12 ) 
51 H 


4-67 ( 15S ) 
3-93( 6 ) 
2-58 ( 24 ) 
1-58 ( 46 ) 
85 (") 
64 (*>) 


1-09 
1-16 
1-40 
1-16 
1-42 
1-25 



It will be seen that here also there is the same marked relation between the 
potential gradient and the dissipation; but the relation between the potential 
gradient and the value of the ratio q does not appear so clearly. Nevertheless, the 
table does not disprove that the ratio rises with the potential gradient, there is 
rather some support given. In the first place there is a distinct rise in the ratio 
over the range from 50 to 200 volts/metre, and the highest value found falls between 
300 and 400 volts/metre. When the whole year is taken into account there are only 
two out of the six divisions which do not conform to the rule. 

Potential Gradient and lonization. So far no results have been published 
showing the relation between potential gradient and ionization, so that the results 
given in the following table cannot be compared with previous work. 

TABLE VIII. Potential Gradient and lonization. 





1 


Winter. 




E 


Summer. 






Year. 




Potential 




















gradient. 






















I_. 


I+. 


r. 


I_. 


I+. 


r. 


I_. 


I + . 


r. 






















volts/metre. 




















50 to 100 


35( 53 ) 


42 ( 52 ) 


1-20 


42 ( 84 ) 


44(84) 


1-07 


39 ( 137 ) 


43(136) 


I'll 


100 150 


29( 52 ) 


34(53) 


ri5 


35 () 


42 ( 48 ) 


1-18 


32( 100 ) 


.37(101) 


1-15 


150 200 


28 ( 34 ) 


33 ( 30 ) 


1-26 


27 ( 4 ) 


37 ( 4 ) 


1-41 


28 ( 38 ) 


36 ( 34 ) 


1-28 


200 300 


19( 25 ) 


24() 


1-26 


17 () 


30 (*) 


1-74 


19 ( 3 ) 


26 ( 26 ) 


1-42 


300 400 


15 C) 


15 C) 


1-00 









15 () 


15 O 


1-00 


400 500 


12 () 


14 (*) 


1-22 











12 () 


14 () 


1-22 


>500 


12 () 


10 ( 3 ) 














12 () 


10 () 






The first striking fact which this table shows is the great dependence of the 
potential gradient on the ionization ; this we might have expected from the 
dissipation results already considered. 

* These small numbers in brackets give the number of observations from which the mean is drawn. 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 



75 



High values of the ionization accompany low values of the potential gradient and 
vice versa. 

Here we find that the ratio between positive and negative ionization (r) does 
increase with the potential gradient over the range from 50 to 300 volts/metre. That 
there is not the same agreement higher is to be expected from the fact that for 
values of the potential gradient over 300 volts/metre the ionization is so small as to 
be only just within the power of the instrument to measure, and so one cannot expect 
the ratio of the observations to be given with any degree of accuracy ; also the 
number of observations with the potential gradient over 300 volts/metre is so small 
that better results could hardly be expected. 

We may, then, take it that the ionization and dissipation have a great determining 
influence on the potential gradient, and that high values of the potential gradient 
are, on the whole, accompanied by high values of the ratio r and q. 

Ionization and Dissipation. It has already been stated that the values of the 
dissipation, as given by ELSTER and GEITEL'S instrument, depend mainly on the two 
factors ionization and wind strength. It would be of considerable interest to find 
how the dissipation varies with either of these factors, the other remaining constant. 

When the greater part of my observations of the dissipation were made. EBERT'S 
instrument was also in use, and gave the true value of the ionization at the time 
when each observation of the dissipation was taken. In order to find how the 
dissipation varies with variations of the ionization, the wind strength being constant, 
I separated out all the results of the dissipation obtained with a given wind strength, 
then divided these again according to the values of the ionization observed at the 
same time. The results are given in Table IX., and have been plotted in fig. 4. 




IO N IZ ATI. ON 



Fig. 4. 

L 2 



76 



ME. GEOKGE C. SIMPSON ON THE 



TABLE IX. lonization and Dissipation according to Wind. 





Dissipation. 


lonization. 


Wind 0-1. 


Wind 1-2. 


Wind 2-3. 


0--1 


.45(12) 


65 () 





1--2 


60( 5a ) 


1-08( 1( >) 





2--3 


l-26( 38 ) 


l-85( 20 ) 


2-70( 16 ) 


3--4 


2-04 C 28 ) 


2-92( 17 ) 


3-88( 47 ) 


4--5 


3-03( 44 


3-83( 33 ) 


5-33( 54 ) 


5--6 


3 36 ( 24 


4-48 ( 6 ) 


5-90( 14 ) 


6--7 


3-56 ( 4 




_ 



We see that, allowing a large margin for the uncertainties of such an investigation, 
the dissipation may be regarded as a linear function of the ionization for any given 
wind strength. It must be remembered that this agreement is only true when 
dealing with a large number of observations ; for the mobility of the ions affects the 
dissipation considerably. It would be interesting to compare individual observations 
of the ionization and the dissipation when the wind strength was accurately known. 
In that case the effect of the mobility of the ions would be very apparent. My 
observations do not allow of this being done, as the wind strengths were only roughly 
judged by the " feel " of the wind, and no doubt varied very much more amongst 
themselves than the mobility did. For the same reason it is of no use finding from 
my observations how the dissipation varied with the wind strength, the ionization 
being constant ; for my classification of the wind strengths, although based on the 
Beaufort scale, would almost certainly differ from a similar classification made by 
another observer. 



Relation between the Meteorological and Electrical Conditions of the 

Atmosphere. 

dissipation and Wind. After what has been already said about the method of 
estimating the wind strength, the following table cannot be regarded as final ; but 
as it shows the influence of the wind as found from all the observations it is printed 
here. It is of considerable interest to notice that the ratio q falls as the wind 
strength increases. 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 



77 



TABLE X. Dissipation and Wind. 



Wind. 


Winter. 


Summer. 


Year. 


Beaufort 








Scale, 




















0-12. 


a+. 


a_. 


2- 


a+. 


a_. 


2- 


a + . 


a_. 


9- 


0-1 


85( 10 ) 


1-04( 108 ) 


1-22 


2 -68 H 


3 -16 (^ 


1-18 


1-44( 15 ) 


1-71 ( 15S ) 


1-19 


1-2 


1-84 ( 45 ) 


2-21 ( 46 ) 


1-20 


3-71 C 23 ) 


4 30 ( 23 ) 


1-16 


2-48 ( 8S ) 


2-91 ( 6y ) 


1-17 


2-3 


3-64 ( 30 ) 


3-99 ( 27 ) 


1-09 


4-62 ( 52 ) 


5-20( 50 ) 


1-13 


4-26 ( 82 ) 


4-78 (") 


1-12 


3-4 


4-45 ( 21 ) 


4-85 ( 25 ) 


1-09 


5-11 ( 44 ) 


5-58( 43 ) 


1-09 


4-90 ( 5 ) 


5-40 ( 8 ) 


1-10 


>4 


5-80 ( 20 ) 


5-96 ( 2S ) 


1-03 


6-05( 36 ) 


6-78 ( 33 ) 


1-12 


5-97 ( 56 ) 


6-44 ( M ) 


1-08 



Dissipation and Relative Humidity. GOCKEL* has gone very fully into the 
relation between dissipation and relative humidity, and his results, which have in the 
main been confirmed by ZoLSS,t show that the dissipation decreases with a rise in 
the relative humidity, and as the dissipation of the positive electricity decreases 
more rapidly than that of the negative, the ratio q increases as the relative humidity 
rises. 

TABLE XI. Dissipation and Relative Humidity. 





Winter. 


Summer. 


Year. 


Relative 








Humidity. 






















a+. 


a_. 


? 


a + . 


a 


2- 


+. 


_. 


* 


per cent. 

30 to 40 


_ 


_. 


_ 


4-61 ('") 


4-97 ( 1C ) 


1-08 


4-G1 ( lt; ) 


4 97 ( ll! ) 


1-08 


40 50 











4-71 ( U3 ) 


5-23( 03 ) 


1-11 


4-71 ( 63 ) 


5-23 ( (i3 ) 


I'll 


50 60 











4-68( 52 ) 


5-49f 2 ) 


1-17 


4-68( S2 ) 


5-49 ( 52 ) 


1-17 


60 70 


3-03( 22 ) 


3 '55 ( 22 ) 


1-17 


3-88( 37 ) 


4-53 ( 37 ) 


1-17 


3-56( MI ) 


4-16H 


1-17 


70 80 


2-61 ( 42 ) 


3-01 ( 42 ) 


1-16 


2-90H 


3-37H 


1-16 


2-73( 71 ) 


3-16 ( 71 ) 


1-16 


>80 


l-37( 51 ) 


1-71 (") 


1-25 




. 




1 37 ( 51 ) 


1-71() 


1-25 



Table XI. shows that for relative humidities greater than 50 per cent, my results 
agree with GOCKEL'S, the decrease in the dissipation as the relative humidity rises 
being very marked, and the value of q also increases as the relative humidity 
increases. But it should be remarked that the fall in the dissipation as the relative 
humidity rises is not entirely due to the relative humidity, for the conditions in 
Karasjok were such that nearly all values of the relative humidity higher than 
80 per cent, were accompanied by a calm atmosphere, and in the main low values 
of the relative humidity were accompanied by high wind. 

Dissipation and Temperature. ZOLSS (loc. cit.) has shown that the dissipation in 
the free air increases with the temperature, and he found that the variation was linear 



* 'Phys. Zeit.,'4, p. 871, 1903. 
t 'Phys. Zeit.,' 5, p. 108, 1904. 



78 



MR. GEORGE C. SIMPSON ON THE 



over the range he investigated. Later GOCKEL returns to this point * and throws 
out the suggestion that the increase in the dissipation is due to the increase which 
the ozone in the atmosphere undergoes as the temperature rises. In Karasjok the 
temperature fell so low during the winter that I was able to observe the influence 
of temperature on the dissipation at very much lower temperatures than had ever 
been done before, obtaining sixty observations with the temperature between - 40 
and - 20 C. Table XII. shows the results, which, in the main, confirm ZOLSS'S 

TABLE XII. Dissipation and Temperature. 







Winter. 




I 


Summer. 






Year. 




Temperature. 






















a+. 


a 


? 


a + . 


a_. 


<! 


+ 


a_. 


2- 


C. 
<-20 

- 20 to - 15 
-15 -10 


-76(28) 

99 ( 34 ) 
1-51 M 


91 ( 31 ) 
l-22( 34 ) 
l-73( 39 ) 


1-19 
1-24 
1-15 











. 76 (28) 

99( 84 ) 
1-51 ( 3! >) 


91 (i) 
1-22 ( S4 ) 
l-73( 39 ) 


1-19 

1-24 
1-15 


- 10 - 5 


2 45 ( 44 ) 


2-82 ( 44 ) 


1-16 











2 45 ( 44 ) 


2-82( 44 ) 


1-16 


- 5 
5 


3-17( 63 ) 
4 34 ( 18 ) 


3-75( C4 ) 
4- 66( 20 ) 


1-18 
1-07 


3-99( 10 ) 
3-71 ( 37 ) 


4-71 H 
3-73( 37 ) 


1-18 
1-01 


3 28 ( 73 ) 
3-92 ( 56 ) 


3 90 ( 74 ) 
4-06( 57 ) 


1-19 
1-03 


5 10 






. 


4-41 H 


4-99( so ) 


1-13 


4-41 ( 80 ) 


4- 99( 80 ) 


1-13 


10 15 











4-68( 66 ) 


5-23( 66 ) 


1-12 


4-68( 6 ) 


5-23( 06 ) 


1-12 



observations. The temperature has a great effect on the dissipation, for it rises from 
83 with temperatures between 40 and 20 C. to 4'95 with temperatures 
between 10 and 15 C., and when the results for the whole year are considered the 
relation is practically linear. But here again attention must be called to the fact 
that the very low temperatures were always accompanied by calm weather ; and 
that there was very much more wind during the summer when the high temperatures 
were obtained than during the winter with its low temperatures. It is interesting to 
note that temperature has no apparent effect on the ratio q. 

lonization and Relative Humidity. It will be seen from Table XIII. that when 
the whole year is taken into account the effect of the relative humidity on the 
ionization is very similar to its effect on the dissipation. That is, the amount of 
ionization decreases with an increase in the relative humidity, while the ratio r 
increases. But it is very interesting to note that when the winter and summer 
results are taken separately this effect is hardly apparent at all. No definite effect 
of the relative humidity on the positive ionization can be detected during either the 
winter or summer six months. While the negative ionization is slightly affected 
during the winter, no effect can be seen during the summer. Nevertheless, during 
both winter and summer the value of the ratio r increases regularly with the relative 
humidity. 

* ' Phys. Zeit.,' 5, p. 257, 1904. 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 



79 



TABLE XIII. lonization and Relative Humidity. 





Winter. 


Summer. 


Year. 


Relative 








humidity. 






















I_. 


!+ 


r. 


I_. 


I + - 


r. 


I_. 


IH-. 


r. 


per cent. 




















30 to 40 











45 (6) 


45 () 


1-04 


45 () 


45 (6) 


1-04 


40 50 











38( 44 ) 


41 () 


1-10 


88() 


41() 


1-10 


50 60 


32 ( 15 ) 


35 ( 15 ) 


1-09 


37( 62 ) 


42 () 


1-14 


SSMj 


40 ( 7 ) 


1-13 


60 70 


28( 24 ) 


32 ( 24 ) 


1-15 


39 ( 34 ) 


45 ( 34 ) 


1-15 


34(58) 


40 ( 58 ) 


1-15 


70 80 
>80 


28( 32 ) 
23(") 


33( 32 ) 
32( 17 ) 


1-16 
1-39 


48(8) 


55 ( 8 ) 


1-20 


32( 40 ) 
28() 


37 ( 40 ) 
32 ( 17 ) 


1-18 
1-39 



lonization and Temperature. From Table XIV. it will be seen that temperature 
has a great effect on the ionization the ionization at temperatures lower than 
20 C. being only a little greater than a third of those with temperatures between 
10 and 15 C. No effect of temperature on the ratio r is apparent. 

TABLE XIV. lonization and Temperature. 



Temperature. 


Winter. 


Summer. 


Year. 






















I_. 


I+. 


r. 


I_. 


I + . 


r. 


I_. 


u. 


;. 


C. 
<-20 


16( 10 ) 


18 () 


1-12 




_ 


_ 


16( 10 ) 


18 () 


1-12 


-20 to -15 


18( 26 ) 


22 ( 24 ) 


1-23 











' 18 ( 26 ) 


22( 24 ) 


1-23 


-15 -10 


22 ( 27 ) 


26 ( 26 ) 


1-18 











22( 27 ) 


26( 26 ) 


1-18 


-10 - 5 


30( 41 ) 


36( 38 ) 


1-20 











30( 41 ) 


36( 38 ) 


1-20 


- 5 


32 (5) 


39( 53 ) 


1-27 


31 ( 21 ) 


37H 


1-19 


31 (") 


39 ( 74 ) 


1-24 


5 


36( 31 ) 


42 ( 29 ) 


1-16 


36 ( 40 ) 


39 ( 40 ) 


1-07 


35('i) 


40(69) 


1-12 


5 10 











40( 6(i ) 


45 ( 66 ) 


1-13 


40 () 


.45(66) 


1-13 


10 15 











43( 28 ) 


45(28) 


1-06 


43( 28 ) 


45(28) 


1-06 



In discussing the effect of temperature on dissipation it was stated that the 
absence of wind at low temperatures might account for the decreased dissipation ; 
but we now see that the smallness of the dissipation is more likely caused by the low 
ionization at low temperatures. 

Potential Gradient and Temperature. It has already been shown that the 
potential gradient varies very greatly with the ionization and dissipation. As we 
have also seen that the ionization and dissipation depend greatly on the temperature, 
we should expect the temperature to have an effect on the potential gradient. That 
such is the case can be seen from Table XV. The potential gradient is high with 
low temperatures and low with high temperatures. This fact has often been noticed 
and recorded before. 



80 



ME. GEOKGE C. SIMPSON ON THE 
TABLE XV. Potential Gradient and Temperature. 





Potential gradient, volts/metre. 


Temperature. 


Winter. 


Summer. 


Year. 


- 40 to - 30 


256 ( 29 ) 


_ 


256 () 


- 30 - 20 


259 ( 65 ) 





259 ( 65 ) 


-20 -10 


235 (') 


. . 


235 ( 117 ) 


-10 


158 ( 178 ) 


126 ( 40 ) 


152 ( 21S ) 


10 


108 ( 45 ) 


105 ( m ) 


106 ( 21fl ) 


10 20 





98 ( 79 ) 


98 ( 97 ) 



The Aurora and the. Electrical Conditions of the Atmosphere. 

During the whole of my stay in Karasjok I could not detect the slightest effect of 
the aurora on any of the electrical conditions of the atmosphere, and most careful 
watching of the needle of the self-registering electrometer did not show any relation 
between potential gradient and the aurora. On first starting my observations I 
thought I found, as many other observers have done, an unsteadiness of the potential 
gradient during an aurora display, but longer experience showed that this unsteadiness 
had nothing to do with the aurora. In order for an aurora to be visible it must be a 
clear night, and a clear night is generally accompanied by low temperature and a 
high potential gradient. The high potential on clear cold nights was always unsteady 
and varied quite irrespective of the presence or absence of an aurora. When an 
aurora was visible naturally it often appeared as if a change in the aurora was 
coincident with a change in the potential gradient, but the attempt to connect 
changes in the potential gradient with changes in the aurora over any length of time 
always failed. Other observers have recorded negative potential gradient during an 
aurora display ; but during the whole winter my self-registering electrometer did not 
once record any such reversal. 

CONCLUSIONS TO BE DRAWN FROM THE WORK. 

The first and most important conclusion is that the difference in the electrical 
conditions of the atmosphere between mid-Europe and this northerly station can all 
be accounted for by the difference in the meteorological condition at the two places. 

Dissipation. For reasons which have been set out above, the actual numbers 
obtained for the dissipation cannot be compared directly with those of other observers, 
but one is quite safe in saying that they are of the same order as those obtained 
further south under the same meteorological conditions. They certainly do not show 
that great increase in dissipation and unipolarity which has been ascribed to places of 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 81 

high latitude by some writers, who base their general conclusions on a few observations 
made by ELSTEE.* 

lonization. At the time of writing no similar series of observations made with 
EBERT'S apparatus have been published, so it is impossible to compare the ionization 
in high latitudes with those in lower. But judging from my own experience, as with 
the dissipation there is no change in the ionization which cannot be explained by the 
meteorological conditions. There is certainly no abnormal ionization nor abnormal 
unipolarity, both the ratios q and r being in excellent agreement with those found in 
Germany. 

The yearly course of the ionization is of great interest and of much importance. 
What causes the yearly variation is not at first obvious. The ionization of the 
air at any moment is determined by two factors : firstly, the rate at which ions 
are produced in the air, and secondly, by the rate at which they re-combine.t The 
yearly variation of the ionization must be caused by variation in either one or both 
of these factors. We do not yet know what the ionizing influences at work in the air 
are ; but possible ones are radio-emanation, the sun's light, and temperature. But 
none of these undergo a yearly change corresponding to that of the ionization. It 
will be shown later that the yearly course of the radio-active emanation in the air is 
exactly opposite to that of the ionization. The sun's light and the temperature both 
have a yearly course in some agreement with that of the ionization, but the maxima 
and minima do not agree : the maximum and minimum of the ionization fall two 
months behind those of the sun's light and one month behind those of the temperature. 
We should then rather expect to find a cause for the variation by assuming a constant 
ionizing factor and looking for a change in the conditions which affect the 
re-combination of the ions. One of the first things which ELSTER and GEITEL found 
when working at the ionization of the air was that the dissipation depends to a great 
extent on the clearness of the air. This factor in itself is capable of accounting for 
the yearly course of the ionization at Karasjok. 

All who have travelled in Arctic regions know the peculiar haze which fills the air 
when the temperature falls very low and gives the " cold " aspect to Arctic scenes. 
Such a haze, which is not a mist or fog, was frequent during the winter at Karasjok. 
On the other hand, at the end of the summer the air reached a degree of 
transparency which I have never seen equalled in any other place. On going into 
the open air one was often struck with the great transparency of the atmosphere, 
giving sometimes the impression that the air between one and distant objects had 
been entirely removed. That it is the transparency of the air rather than the 
temperature which determines the ionization could often be seen from individual 
observation. On June 16 the temperature rose to the abnormal value of 247 C., 
the air being exceedingly hazy and oppressive ; the ionization was only '18, the mean 

* 'Phys. Zeit.,' 2, p. 113, 1900. 

t SCHUSTER, 'Proc. Man. Lit. and Phil. Soc.,' vol. 48, Part II., p. 1, 1904. 
VOL. CCV. A. M 



82 ME. GEOEGE C. SIMPSON ON THE 

for the month of June being "39. On September 19 the temperature rose to 
16-4 C., after having been below 5 for the previous few days; the air again was very 
hazy and sultry and the ionization went down to '24, the mean for the month 
being '44. On the contrary, a clear day in the winter would be accompanied by 
comparatively high value of the ionization : February 22 ionization '40, mean for 
month, -21. Much to my regret I cannot support this conclusion by actual figures, as 
Karasjok was so enclosed by low hills that it was impossible to obtain even a rough 
arbitrary scale of the clearness of the air by the visibility of distant objects. But 
there can be no doubt that the maximum of the transparency of the atmosphere 
corresponded with the maximum of the ionization. 

Potential Gradient.The yearly course of the potential gradient in Karasjok 
conforms to the general rule for the northern hemisphere formulated by HANN* in 
the following words : " The maximum of the potential gradient occurs in December, 
January or February ; it falls rapidly in the spring ; remains nearly at the same level 
during the summer and then rapidly rises again in October and November." 

The fact that the potential gradient runs so exactly opposite to the dissipation 
makes it appear as though there were a constant charge of negative electricity being 
continually given to the surface of the earth during the whole year, and that the 
amount at any moment on the surface itself (measured, of course, by the potential 
gradient) is determined by the rate at which the charge is being dissipated. How 
this charge is supplied to the earth still remains, in spite of many theories, one of the 
unsolved problems of atmospheric electricity. 

Two types of daily variation of the potential gradient are known, t The first is a 
double period, having a minimum between 3 and 5 A.M. and a second about midday, 
the corresponding maxima falling at about 8 A.M. and 8 P.M. Good examples ot 
this are Batavia and Paris. The other type consists of a single maximum and 
minimum, the former falling in the evening and the latter between 3 and 5 A.M. To 
this type belong the records made at high altitudes and at some places during the 
winter. 

The daily course of the potential gradient for the whole year at Karasjok belongs 
to the latter class, there being only one maximum and one minimum. Taking the 
four seasons each by itself, we see that the winter and spring curves are of the same 
type, while that for the summer shows a slight tendency to form a minimum at 
midday, and the autumn curve has a distinct double period. As stated above, the 
morning and evening maxima of the autumn curve were considerably strengthened by 
the mists which formed over the river. The nearest place to Karasjok at which 
measurements have been made of the potential gradient is SodankylaJ in Finland, 
and the curves for the two places are in surprising agreement. 

* ' Lehrbuch der Meteorologie,' p. 715. 

t HANN, 'Lehrbuch der Meteorologie,' p. 716. 

} ' Expedition polaire, 1882-83.' 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 83 

It would appear from these results as though the double daily period were confined 
to places having a large daily temperature variation. The daily variation of the 
temperature was much the greatest in Karasjok during the autumn three months : 
the sun not rising during the winter three months, not setting during the summer 
three months, and the snows still being on the ground during the spring, all tended 
to keep the daily temperature variations low during these seasons. In all places 
having a double daily period of the potential gradient the midday minimum is 
always greater during the summer than during the winter, which supports the same 
conclusion. 



ATMOSPHERIC RADIO-ACTIVITY. 

In 1901 ELSTER and GEITEL* made the very important discovery that the 
atmosphere always contains more or less radio-active emanation. Since the discovery 
several workers have repeated the observations and confirmed the results. During 
the whole of 1902 ELSTER and GEITEL t made daily observations of the radio-activity, 
and found that the amount of emanation in the atmosphere depends largely on some 
meteorological conditions, such as the rising or falling of the barometer and tempe- 
rature ; and, as a result of their work, made the suggestion that the emanation in the 
air is supplied entirely by the radium or radio-active emanation contained in the soil. 

The method used by ELSTER and GEITEL to detect and measure the emanation in 
the air, which has been adopted by other observers, consisted of stretching a wire 
about 10 metres long between insulators in the open air. This wire was then charged 
to a negative potential of between 2000 and 2500 volts. After the wire had been 
exposed to the air at this potential for two hours, it was removed and wrapped round 
a net cylinder fitting inside the "protection cylinder" attached to their dissipation 
apparatus (specially closed at the bottom as well as the top for this measurement), 
and the rate at which the electroscope discharged was determined. When one metre 
of the wire discharged the electroscope one volt in one hour the atmospheric activity 
was said to be unity and written A = 1. 

Using ELSTER and GEITEL'S method, I made observations of the atmospheric radio- 
activity in Karasjok. I first started by making odd observations every now and 
again, but found that the values obtained were so much higher than anything which 
had up to that time been recorded that I determined to make a thorough investi- 
gation of the matter. In December, 1903, 1 started a series of observations, observing 
three times each day. As each observation occupied over two hours, it was impossible 
to take them so frequently without interfering with my other work, therefore I 
decided to take three observations each day for a month, then wait a month, then 

* ' Phys. Zeit.,' 2, p. 590, 1901. 

t ' Phys. Zeit.,' 4, p. 526, 1903. 

M 2 



84 



ME. GEORGE C. SIMPSON ON THE 



repeat them the following month, and so on. This was done for the whole year with 
the exception of the summer months, when observations were made alternate weeks 
instead of alternate months. Besides the three observations during the day, for one 
week out of every four I continued the observations during the night, observing 
between the hours of 3 and 5 A.M. 

In order not to interfere with my other observations, the observations of the radio- 
activity had to fit in between them, and the following times were chosen as being 
the most convenient : Night observation from 3 to 5 A.M. ; morning observation from 
10 to 12 A. M. ; afternoon observation from 3 to 5 P.M. ; and evening observation from 
8.30 to 10.30 P.M. In this way it proved possible to get a good idea of the yearly 
and daily course of the radio-activity. From the 420 separate observations the effect 
of the different meteorological conditions have been obtained. 

As the value of the radio-activity varied very greatly from month to month, in all 
the following tables each month is treated by itself, and then the whole year treated 
in a separate column. 

TABLE XVI. Kadio-activity. 





Mean values. 


Mean 
values. 


Maximum values. 


Early 

morning, 

3-5 A.M. 


Morning, 

10-1 2 A.M. 


After- 
noon, 
3-5 P.M. 


Evening, 
8.30- 
10.30P.M. 


Early 
morning. 


Morning. 


After- 
noon. 


Evening. 


*November ~| 
and ^ 
December J 


209 (") 


87 (2<t) 


88 ( 2 *) 


131 (22) 


129 


396 


204 


384 


432 


February . 


221 () 


72 (23) 


113 (2*) 


101 (2-*) 


127 


366 


234 


342 


228 


April . . . 


87 () 


41 (23) 


37 (23) 


55 (22) 


55 


210 


120 


90 


120 


May and "1 
June j 


79 () 


35 (20) 


32 (20) 


43 (20) 


47 


204 


102 


78 


108 


July and "1 
August J 


175 ( 6 ) 


35 (2) 


32 (20) 


76 (*>) 80 


270 


72 


93 


198 


September . ; 


201 ( 6 ) 


81 (is) 


70 (is) 


142 (18) 123 


390 


156 


122 


264 


Year . . . 


162 (36) 


58 (128) 


62 (129) 


92 (126) , 93 


396 


234 


384 


432 



* For the observations of this month set out in full detail see 'Boy. Soc. Proc.,' vol. 73, p. 209, 1904. 



ATMOSPHEEIC ELECTRICITY IN HIGH LATITUDES. 



85 



Table XVI. gives the mean and maximum values of the activity for each month. 
From it the yearly course is seen to consist of two periods. During the first, 
extending from the beginning of September to the end of February, the radio-activity 
is constant and very high. During the other months the activity is much lower (less 
than half) and not quite so constant. The maximum falls in midwinter and the 
minimum in midsummer. A distinct daily period is also shown : the maximum falling 
in the early hours of the morning and the minimum about midday. 

Table XVII. shows the effect of temperature on the radio-activity. It is interesting 
to notice that from the results for the whole year the temperature appears to have a 
very marked effect on the radio-activity ; but when each month is taken by itself, 
the effect is not apparent at all. It would appear from this that temperature only 
plays a secondary part in determining the amount of activity in the air. 



TABLE XVII. Radio-activity and Temperature. 



Temperature. 


November 
and 
December. 


February. 


April. 


May and 
June. 


July and 
August. 


September. 


Year. 


"0. 
<-30 


127 ( 12 ) 


98 () 










113 ( 23 ) 


- 30 to - 20 


166 ( 10 ) 


126 ( 34 ) 











135 () 


-20 -10 


80 (i 7 ) 


96 ( 20 ) 











88 () 


- 10 82 ( 25 ) 


66 ( 12 ) 


51 () 








271 ( 4 ) 78 (s) 


10 110 ( 8 ) 





47 ( 4li ) 


33 ( 41 ) 


62 ( 33 ) 


100 ( 44 ) 63 ("2) 


10 20 











56 ( 19 ) 


56 ( 30 ) 


83 ( 12 ) 61 ( 61 ) 


>20 











39 () 


65 (3) 


48 O 



The relative humidity appears to have a very large effect on the radio-activity, for 
not only can its influence be seen when the year is taken as a whole, but it is very 
apparent in each separate month with the exception of February. 



TABLE XVIII. Radio-activity and Relative Humidity. 

















Relative 
humidity. 


November 
and 
December. 


February. 


April. 


May and 
June. 


July and 
August. 


September. 


Year. 


Per cent. 

<50 




24 (7) 


30 ( 2r ) 


38 ( 22 ) 


53 () 


34 W 


50 to 60 


27 ( 2 ) 


32 ( n ) 


45 ( 10 ) 31 ( 8 ) 


70 (w) 


46 () 


60 70 


54 (ii) 


39 (is) 


43 ( 12 ) 32 ( 9 ) 


86 ( 10 ) 


50 ( 65 ) 


70 80 124 (*7) 


48 ( 23 ) 


43 ( 8 ) 51 () 


97 H 


88 ( 102 ) 


80 90 
>90 


, 


90 (") 
60 (i) 


63 (n) 
85 () 


75 M 

40 ( 2 ) 


143 ( 9 ) 
170 (8) 


156 (n) 
196 ( 8 ) 


106 (6i) 
132 ( 22 ) 



8fi ME. GEOKGE C. SIMPSON ON THE 

on 

The wind strength has a most direct influence, which can not only be seen in the 
year and separate months, but can also be detected in nearly all the individual 
observations. 

TABLE XIX. Kadio-activity and Wind Strength. 



Wind 
(Beaufort Scale). 


November 
and 
December. 


February. 


April. 


May and 
June. 


July and 

August. 


September. 


Year. 


0-2 


116 ( 49 ) 


110( 68 ) 


65 ( 32 ) 


57 H 


81 () 


126 () 


98 C 267 ) 


3-4 
5-6 


79 H 
63 () 


66 ( 7 ) 

54 ( 2 ) 


36 ( 22 ) 
34 ( 16 ) 


33 ( 20 ) 
27 () 


35 ( 22 ) 
39 ( 2 ) 


67 ( 13 ) 
60 ( 4 ) 


47 ( 97 ) 
40 () 


>6 


32 ( 3 ) 





21 ( 3 ) 


10 () 


20 () 


114 ( 3 ) 


33 ( 21 ) 



The radio-activity is greater with a falling than with a rising barometer. The 
results show this every month without exception. 

TABLE XX. Radio-activity and Barometer. 



Barometer. 


November 
and 
December. 


February. 


April. 


May and 
June. 


July and 
August. 


September. 


Year. 


Rising .... 
Falling. . . . 


95 ( 44 ) 
115( 23 ) 


97 ( 34 ) 
119 ( 34 ) 


38 ( 29 ) 
53 ( 40 ) 


25 ( 26 ) 
53 ( 40 ) 


50 ( 42 ) 
77 ( 23 ) 


107 ( 27 ) 
110( 28 ) 


71 ( 201 ) 
85 ( 19 ) 



But this does not necessarily mean that the radio-activity is greater with a low 
than with a high barometer. Table XXI. shows that such is not the case. Out of 
the six separate periods only two, April and May and June, show a regular increase in 
the radio-activity as the height of the barometer decreases. In the other months, and 
for the year considered as a whole, no relation appears between the radio-activity and 
the height of the barometer. 

TABLE XXI, Radio-activity and Height of the Barometer. 



Barometer. 


November 
and 
December. 


February. 


April. 


May and 
June. 


July and 
August. 


September. 


Year. 


minims. 

>760 
760 to 750 


137 ( 20 




73 ( 14 ) 
104 (is) 


30 ( 2 ) 
39 ( 1S ) 


29 ( 25 ) 


74 ( 9 ) 


158 ( 5 ) 
102 ( 33 ) 


89 ( 2i ; 
81 ( 126 


} 


750 740 
740 730 


85 ( 23 
109 (" 




93 ( 29 ) 
146 ( 2 ) 


42 () 
65 ( 23 ) 


44 ( 32 ) 
57 ( 9 ) 


53 ( 86 ) 
50 ( 9 ) 


104 ( 28 ) 


65 ( 174 
93 ( 79 




730 720 


66(i 




102 (i) 












70 ( 





ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 



87 



An uncertain result is obtained when the observations are divided according to the 
amount of cloud. For the whole year and for two of the separate months the clouds 
appear to have a direct influence on the radio-activity, but during the other four 
months there does not appear to be any relation between the two. 

TABLE XXII. Radio-activity and Clouds. 



Clouds. 


November 
and 
December. 


February. 


April. 


May and 
June. 


July and 
August. 


September. 


Year. 


0-3 

4-7 
8-10 


130 ( 18 ) 
107 ( 26 ) 
76 ( 2r ) 


120 () 

124 ( 17 ) 
96 ( 2r ) 


34 () 
61 () 

46 ( 5 ) 


30 (<0 
49 ( 13 ) 
39 ( 46 ) 


117 O 
102 ( 16 ) 
42 () 


172 ( 7 ) 
96 ( 2 ) 
102 ( 33 ) 


114 ('*) 
93 ( 107 ) 
62 ( 22 ) 



The direction of the wind appears to have an influence on the radio-activity, for 
the latter is at a maximum with a south wind and a minimum with a north wind. 
It is very questionable if this is a real effect or only a re-statement of the relation 
between radio-activity and a rising or falling barometer, for every case of a north 
wind was accompanied by a rising barometer and nearly every case of a south wind 
by a falling barometer. That it is not the other way about is seen from the fact 
that observations taken with no wind show an unmistakable relation between the 
radio-activity and a rising or falling barometer. 

TABLE XXIII. Radio-activity and Wind Direction. 



Wind strength. 


N: 


S. 


E. 


W. 


Greater than 3 on the Beaufort scale . . . 


25 ( 4S ) 


53 ( 57 ) 


28 ( 4S1 ) 


47 () 



No relation between the radio-activity and potential gradient can be detected 
either in the separate months or the whole year. 

TABLE XXIV. Radio-activity and Potential Gradient. 



Potential Gradient. 


November 
and 
December. 


February. 


April. 


May and 
June. 


July and 
August. 


September. 


Year. 


Negative potential 


33 ( 6 ) 




41 ( 4 ) 


24 (!) 


42 ( 2 ) 


137 ( 2 ) 


49 ( 15 ) 


to 100 volts/metre 


106 (w) 


148 ( 18 ) 


51 ( 2 -) 


24 ( 42 ) 


59 ( 35 ) 


100 ( 40 ) 


77 ( m ) 


100 200 


143 ( 25 ) 


119 ( 29 ) 


51 ( 37 ) 


34 () 


61 ( 28 ) 


134 ( 15 ) 


86 ( 166 ) 


200 300 


90 ( 10 ) 


90 ( 10 ) 


32 ( 4 ) 










81 ( 24 ) 


300 400 


71 ( 10 ) 


64 () 


51 ( 2 ) 











66 ( 18 ) 


>400 


83 ( 3 ) 


61 ( 16 ) 


31 () 











58 ( 24 ) 



88 MR. GEORGE C. SIMPSON ON THE 

I found it impossible to make observations of the ionization and dissipation at the 
same time as those of the radio-activity. This is much to be regretted, as it is very 
important to decide if the emanation in the atmosphere is the cause of the permanent 
ionization. That the ionization does not depend on the amount of emanation alone is 
quite clear from the yearly variations of the two, for the ionization is at a minimum 
during the winter, exactly the season when the activity is at its maximum. But that 
does not prove that the ionization is not due to the emanation ; we can only say that 
if it is, then the increase in the production of ions owing to the excess of emanation is 
overbalanced by the increased rate of recombination due to the winter conditions. 

That all the relations shown by the above analysis should be as they are gives an 
exceedingly strong support to ELSTER and GEITEL'S theory of the origin of the 
atmospheric radio-active emanation. According to their theory, the air which is 
mixed up with the soil of the ground becomes highly charged with radium 
emanation.* When the barometer falls, this air passes out of the ground into the 
atmosphere, bringing with it its charge of emanation. 

All the facts of the above analysis receive a very simple explanation by this 
theory if one extends it to include the fact that, as the emanation is a gas contained 
in the soil, it must constantly diffuse into the atmosphere above quite independently 
of the state of the barometer. Assuming this constant diffusion, we at once see that 
everything which tenth to reduce the atmospheric circulation, i.e., to keep the air 
stagnant, tends a/so to increase the quantity of emanation in the lower layers of the 
atmosphere. 

Looking now at each of the tables in order, we see that the temperature does not 
have a direct, but an indirect influence on the radio-activity. This is explained by 
the fact that the low temperature of the winter produces a nearly permanent 
temperature inversion, as mentioned above, which entirely prevents ascending 
currents of air. Thus the emanation on leaving the ground in cold weather cannot 
rise, but collects in the lower atmosphere, causing the high winter values of the radio- 
activity. 

The reason why the radio-activity is high with high relative humidity is easily 
found when one considers that each evening, as the temperature rapidly falls, two 
things happen : first there is a rapid rise in the relative humidity and secondly 
ascending currents of air are cut off. The latter fact gives rise to the high radio- 
activity. Also a mist or fog is always a sign of stagnant air. 

A high wind is naturally accompanied by low activity, for it acts as a stirrer, and 
rapidly mixes the escaped emanation with a large volume of air. 

ELSTER and GEITEL'S theory explains the relation found between radio-activity and 
a rising and falling barometer. If air stream out of the ground when the barometer 
falls, it must charge the atmosphere with its emanation. 

* 'Phys. Zeit., 1 5, p. 11, 1904; 'Terr. Mag.,' vol. 9, p. 49, 1904. 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 89 

The effect of the clouds is not easy to understand, and as the results do not show 
a pronounced dependence of the radio-activity on the clouds, perhaps it is not real, 
unless it is that clouds are usually associated with ascending currents of air. Other 
observers* have found a relation between radio-activity and clouds, but until more 
observations are made the question must be left unsettled. 

Thus we see that the whole effect of the meteorological conditions on the radio- 
activity depends on whether those conditions tend to mix the emanation rapidly with 
a large volume of air, or to keep it near to the ground from which it is always 
escaping. 

The same principles lead us to an explanation of the daily and yearly course of 
the radio-activity. During the daytime ascending currents are formed, while as the 
evening approaches these stop and the air lies cold and stagnant during the night. 
Thus we see why the minimum should be in the daytime and the maximum during 
the night. 

The yearly period has a similar explanation. During the winter in Karasjok, when 
the snow is permanently on the ground, temperature inversion accompanied by 
stagnant air is the rule rather than the exception. On the contrary, during the 
summer when there is nearly permanent sunshine, ascending currents will be formed 
at all times of the day and night. This accounts for the winter maximum and the 
summer minimum of the radio-activity. 

One strange fact is that the activity should be so high during the winter when the 
whole country is covered with snow. This at first led me,t with other observers,^ to 
doubt ELSTER and GEITEL'S theory, but the reason is not hard to find if it is 
remembered that the snow must form a very large reservoir to hold the emanation as 
it is escaping from the soil. It would be interesting to see if air, drawn from the 
snow in the way ELSTER and GEITEL drew it from the ground, would be charged 
with emanation. I wished to test this, but had no instruments with me which could 
be used for the experiment. 

One would also expect high values of the radio-activity in Karasjok during the 
winter from another consideration. Karasjok is situated on the river, and just as the 
water from all the surrounding land flows down to the river, so when the temperature 
falls very low the cold air will also find its way into the river valley. This cold 
air flowing over the ground will sweep the emanation along with it, and so the valley 
will become filled with air highly charged with emanation. 

In order to find if the minerals of Karasjok are particularly rich in radio-active 
constituents I sent samples of sand and rock to the Hon. R. J. STRUTT, who very 
kindly undertook to test them, and to whom my best thanks are due for the trouble 
he took in his investigation of them. In none of the specimens was he " able to 

* GOCKEL, ' Phys. Zeit.' ; ZOLSS, ' Phys. Zeit.' 
t ' Roy. Soc. Proc.,' vol. 73, p. 209, 1904. 
I ' Phys. Zeit.,' 5, p. 591, 1904. 
VOL. CCV. A. N 



90 MR. GEORGE C. SIMPSON ON THE 

detect the emanation with certainty, and none yielded more than a 100 | 000 part of 
what the same quantity of pitchblende would give on heating." Thus the soil 
conditions of Karasjok do not appear to be abnormal, so that the high radio-activity 
found there during the winter must be due to the meteorological conditions being so 
favourable to the collection of the emanation in the lower atmosphere. 

In order to compare the value of the radio-activity at Karasjok with that of other 
places, the only observations which can be used are ELSTER and GEITEL'S,* in 
Wolfenbiittel (mid-Germany), and GOCKEL'S,! in Freiburg (Switzerland) ; no other 
observer has extended his observations over a sufficiently long period to give good 
mean values. Neither ELSTER and GEITEL nor GOCKEL observed between 8 P.M. 
and 8 A.M., and as the values I found between those hours were very much the 
largest it is not right to compare my means with their means, so in what follows 
I use only the values which were obtained during the morning and afternoon 
observations in Karasjok. 

The means for the whole year are Wolfenbiittel 18 '6, Freiburg 84 and Karasjok 60. 
Thus Freiburg is the highest and Wolfenbiittel the lowest. The absolute maxima 
(between 8 A.M. and 8 P.M.) are Wolfenbiittel 64, Freiburg 420, Karasjok 384, i.e., 
the same order as before. 

It is a strange fact that the yearly period should be so marked in Karasjok, while 
no yearly period can be detected in either Wolfenbiittel or Freiburg. As stated 
above, neither ELSTER and GEITEL nor GOCKEL have observed after 8 P.M., so it is 
impossible to compare the daily periods. It would be exceedingly interesting to 
know if there is a large daily variation in mid-Europe, for if there is not, then the 
mean winter value of the radio-activity in Karasjok will be very high compared with 
mid-Europe, the mean for the winter, when night as well as day observations are 
taken into account, being 126 at Karasjok. 

GOCKEL'S maximum observation of 420 was quite an exception, but even that was 
exceeded by my absolute maximum of 432 (observed between 8 and 10 P.M. on 
December 17). With this one exception the values found by GOCKEL did not 
exceed 170, while I found 200 quite a medium value during the winter in Karasjok. 
It would appear, from the results which have already been published, that high 
values of the radio-activity are much more common in Karasjok than in any place 
yet investigated. 

ELSTER and GEITEL measured the radio-activity at Juist, an island in the North 
Sea, and found it only 6, while in the Bavarian Alps they found the high value 
of 137. From this, and their observations in Wolfenbiittel, they concluded that the 
radio-activity increased from the sea inland. In order to find if the same conditions 
held in the north, I stayed in Hammerfest on my way home, and made daily observa- 

* ' Phys. Zeit.,' 4, p. 526, 1903. 
t ' Phys. Zeit,,' 5, p. 591, 1904. 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 



91 



tions of the radio-activity there for four weeks (October 17 to November 12), in 
exactly the same way as I had done in Karasjok. 

The result was in entire agreement with ELSTER and GEITEL'S observations. The 
mean for the month was only 58, which must be compared with the Karasjok winter 
value of 126, the numbers for the different times of observing being 

TABLE XXV. Radio-activity in Hammerfest. 





Early morning, 

3-5 A.M. 


Morning, 

10-12 A.M. 


Afternoon, 
3-5 P.M. 


Evening, 
8.30-10.30 P.M. 


Mean. 


Mean 


97 () 


33 ( 24 ) 


50 ( 24 ) 


52 f-' 4 ) 


58 


Maximum . . . 


204 


156 


252 


- 1 - 1 \ 1 
150 





But what is much more interesting and important is the great variation of the 
radio-activity with the wind direction. When it is remembered that Hammerfest is 
free to the open ocean on the north and west, while to the south lies the whole 
stretch of Norway and Sweden, the following table tells its own story : 

TABLE XXVI. Radio-activity and Wind Direction in Hammerfest. 





North. 


South. 


West. 


Mean 


8 ( 10 ) 


72 ( 30 ) 


4 (io) 


Maximum 


20 


250 


10 



It must be admitted that these results lend great support to ELSTER and GEITEL'S 
hypothesis. 

OBSERVATIONS OF THE AURORA. 

It was not my intention on going north to make a particular study of the aurora, 
but I naturally followed it with as much attention as possible. The necessity of 
making my regular observations during the daytime, beginning at 7.30 A.M., made it 
impossible to stay up to watch the aurora late into the night. Each evening I noted 
down the chief variations in the aurora's form and brilliancy, but did not go into 
minor details. I intend here to shortly record a few of the things which struck me, 
and which are rather of a general than particular interest. 

During the year of my stay there were not many exceptionally fine auroras, and 
coloured auroras were very rare. From the one or two I did see the colours appeared 
to be of two distinct kinds (by colours in this connection I mean colours other than 
the greenish-white light of the ordinary aurora). There is first the mass of coloured 

N 2 



92 ME. GEORGE C. SIMPSON ON THE 

light which retains its form and colour for a comparatively long time, and colours 
which flash out and disappear immediately. A very interesting fact struck me with 
regard to the latter class of colour. It is generally known that an aurora arch is 
often composed of a series of spear-like shafts of light arranged perpendicularly to the 
direction of the arch, and which appear to be in constant motion. A number of these 
spears will suddenly become brilliant and the lower ends shoot out of the arch into 
the black sky below. The brilliancy will then run along the arch like a wave of 
light, lighting up all the spears as it goes along. I noticed that the " front" of such 
a wave of brilliancy and the points of the spears when shooting out were bright red, 
but as soon as the motion stopped the colour disappeared, while the more violent the 
motion the purer and brighter the red. It appeared as if some physical process 
accompanied the passage of the aurora beam through the air and gave out a red 
light. For example, if the air had to be ionized before the discharge could pass 
through, then the process of ionization produced red light. If the motion was 
particularly violent, the production of red light would be followed by a production of 
brilliant green light, so that if a bright wave passed along an arch two waves of 
colour would appear to travel along, first a wave of red light, closely followed by a 
green wave, the two travelling so closely together as to appear one wave having a 
two-coloured crest. Similarly spears shooting out with a great velocity would appear 
to have red and green tips. 

The question of the relation of clouds to auroras has been very often raised. Three 
of my observations bear on this point. 

On the evening of October 11, 1903. after a fairly active display, the aurora 
disappeared ; but its place was taken by a system of narrow bands of cirrus clouds 
stretching right across the sky, which, being illuminated by the bright moon, had all 
the appearances of the aurora. That they did not form part of the aurora could only 
be decided at first owing to no line appearing in the spectroscope when pointed at 
them ; but later there could be no doubt, as they partly obscured the moon. 

On October 26 a very similar phenomenon again appeared ; that which at first was 
taken to be aurora later turned out to be cloud. 

On December 13 the most brilliant aurora display of my stay took place. The 
whole display reached a climax at 9.45, when a most brilliantly coloured corona shot 
out from the zenith. While this final brilliant display was taking place the sky 
suddenly became thinly overcast, and the aurora was only visible later as bright 
patches through the clouds. 

It has long been a matter of controversy as to whether the aurora ever extends 
into the lower regions of the atmosphere. Several observers positively affirm that 
they have seen it quite close to the ground. This may be due to an optical illusion ; 
one evening I was, for a considerable time, in doubt as to whether the aurora was 
really under the clouds or not. All over the sky were detached clouds, the clouds 
and spaces between them being of about the same size and shape. Right across the 






ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 93 

sky a long narrow aurora beam stretched, showing bright and dark patches owing to 
the clouds. It looked exactly as if the aurora beam ran along under the clouds, 
brightly illuminating the patches of cloud which it met. In reality the bright 
patches were the openings and not the clouds. It took me a long time to make 
quite certain of this, and it was only by at last seeing a star in the middle of a 
bright patch that I could be quite certain. 

LEMSTROM strongly supported the idea that the aurora often penetrates down to 
the earth's surface, and described how on one occasion the aurora line appeared in a 
spectroscope pointed at a black cloth only one or two metres away. I was able to 
repeat this observation on several occasions, and found that the line which then 
appeared in the spectroscope was not due to an aurora discharge in the air between 
the spectroscope and the black cloth, but was due to reflected light, which it was 
impossible to prevent entering the spectroscope, as the whole landscape was lit up 
with the monochromatic light of the aurora. 

All the time I observed the aurora I could not detect the slightest noise accom- 
panying the discharge. 

I cannot close this account of my work in Lapland without expressing my deepest 
thanks to each and every one of the small Norwegian colony in Karasjok in 
particular to my host and hostess, Handlesmand arid Fru NIELSEN ; and to Lensmand 
and Fru HEGGE all of whom did their very best to make my stay amongst them a 
source of the greatest pleasure and real enjoyment. 



APPENDIX. 

Potential Gradient. The potential gradient was measured, as stated in the paper, 
by means of a Benndorf self-registering electrometer. The electrometer is of the 
quadrant type, the quadrants being kept at a constant voltage by means of small 
cells, and the needle itself connected to the collector. To the bifilar suspension of 
the needle a long aluminium arm is attached, which swings freely above a strip of 
paper drawn along by clockwork. Every two minutes an electrical contact is made 
which causes a bar to descend and to press the end of the aluminium arm down upon 
the paper, where a dot is left showing the position of the arm and so the potential 
gradient. The zero of the instrument was so arranged that on the normal side a 
potential gradient of 800 volts/metre could be registered. On the negative side 
only 100 volts/metre could be registered; but as all the days on which negative 
potential gradient occurred were disturbed days, and the results on such days not 
used, the range was quite great enough. 

The collector was arranged in the following way : My bed-sitting room in which 



94 MR. GEOEGE C. SIMPSON ON THE 

I had my instrument was a little hut near to my host's large <' handlesmand's " 
house. On the end of the large house was a flag staff, to the top of which I 
attached an insulator and from it took a wire through a window into my room. 
About a third of the way up the wire I attached two milligrams of radium bromide 
which acted as a collector. On the accompanying photograph, the insulator, wire 
and the position of the radium collector are shown. The height of the collector 
above the ground was 5| metres. This arrangement acted extremely well and, as far 
as I could judge, gave as good results as could be wished. 

The potential gradient was reduced to that over a level surface by making 
simultaneous observations with a flame collector and leaf electroscope above the 
most level piece of ground I could find. The country was so rough that a good and 
accurate determination could not be made, but the error is certainly not 20 per cent. 
During the year this reduction was several times repeated, no change being found. 
Great attention was also paid to the insulations, which were never found defective. 
As the collector was situated between two houses over a much frequented road, no 
accumulation of snow took place under it, so corrections due to the height of the 
snow were not necessary. 

Dissipation and lonization. In order to observe the ionization and dissipation 
without being disturbed by the smoke of the village, two platforms (as shown in the 
photograph) were built at different parts of the village, but as both were to the 
north of a large part of the village, I could not observe when a south wind was 
blowing ; with all other winds one of the platforms was on the windward side of the 
houses. The platforms were about a metre above the ground and the instruments 
on a shelf about a metre and half over the platform ; above all was a roof to protect 
the instruments from rain and snow. By this arrangement the instruments were 
exposed to the full force of the wind. In order to read the dissipation electroscope 
in a high wind, a small screen was held to protect the instrument just at the moment 
of observation. 

The usual method of observing the dissipation or ionization is to charge the 
electroscope, take a reading, then return in 15 minutes and take another reading. 
This method is open to great objections : first it is quite easy to make a false reading, 
and secondly in open-air work the leaves are not steady enough to allow of one 
reading being accurate. The method I adopted was to charge the two instruments, 
then take a reading of the dissipation instrument, half a minute later a reading of 
the ionization instrument, then at the minute take another reading of the dissipation 
instrument, at the next half minute a second reading of the ionization instrument, 
and so on for 5 minutes, when of course I had five readings on each instrument. 
Ten minutes later I started reading again, and at minute intervals read each of the 
instruments five times, then from a table found the value corresponding to each of 
the readings, took the mean of the first five, then that of the second five, and used 
these means as single values separated by an interval of 1 5 minutes. In this way 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 



95 





96 ME. GEOEGE C. SIMPSON ON THE 

errors of reading were avoided and errors due to the unsteadiness of the leaves 

greatly diminished. 

After having by this method obtained a measurement, using, say, a positive charge, 
the observation was repeated using a negative charge, and finally another observation 
with a positive charge. The mean of the two positive values, together with the 
negative value, were used as the result of the whole observation. This method I 
found to be absolutely necessary if reliable values of the ratios q and r were to be 
obtained, for both dissipation and ionization undergo great changes in the course of 
the time taken to make an observation. A whole observation when taken in this way 
occupied an hour and a quarter. 

Long experience taught me to know when I could expect difficulties with the 
insulations. On such days, instead of the method sketched above, an observation 
was taken with one charge, and after that the insulation tested for 15 minutes, 
then an observation with the other charge, followed by a final insulation test for 
the same length of time, the whole observation taking about an hour and a half. 

During the summer I had great difficulty in using the Ebert instrument owing to 
the mosquitoes being drawn into the instrument and so discharging the electroscope. 
In June the mosquitoes and other small flies were so numerous that it was quite 
impossible to use the Ebert instrument without some means of keeping the flies out, 
so I attached a funnel-shaped net to the front of the aspirator tube and used the 
instrument so protected. I expected that this net would cause some reduction in 
the value of the ionization as measured by the instrument, so as soon as the 
mosquitoes were sufficiently reduced in number to allow of observations being made 
with the unprotected tube I made a series of observations to find the effect of the 
net. Much to my regret and disappointment I found that the effect of the net 
varied very much according to the wind strength. In perfectly still air the net 
reduced the ionization by nearly a quarter, while with a stiff" breeze it had no effect. 
This made individual observation practically useless, and in all the above tables 
connecting ionization and the meteorological elements all the observations taken 
when the net was in use from June 9 to August 12 have been neglected. 
As the result of a long investigation I concluded that 10 per cent, added to the 
results in the bulk would just about correct for the effect of the net. Eesults so 
corrected are used in the curves and tables showing the yearly course of the 
ionization. 

Radio-activity. In my measurements of the radio-activity, as stated above, ELSTER 
and GEITEL'S method was used. In order to charge the wire to a negative potential 
of between 2000 and 2500 volts, I used a small influence machine, built on the 
principle of a Kelvin replenisher and driven by a falling weight. By means of a 
variable high resistance, consisting of a strip of ebonite, one side of which had been 
rubbed with a black-lead pencil and so mounted in a tube that an earth -connected 
pad could move along it, the potential of the wire could be very easily regulated. 



ATMOSPHERIC ELECTRICITY IN HIGH LATITUDES. 97 

The instrument worked splendidly, and I had very little trouble with it. Its only 
drawback was that it could not be left to itself for more than 20 minutes, for then 
the weight required winding up again, and sometimes the voltage would vary if not 
attended to. 

For my insulators I used amber enclosed in a metal case, so designed that air had 
a long way to travel from the oiitside before it could reach the amber. The 
insulators acted very well even in rain and fog. It was seldom that I had any 
difficulty with them, and I was never compelled to give up an observation on account 
of insulation troubles. 

Meteorological Measurements. Karasjok is a second-order station of the Norwegian 
Meteorological Service, and 1 was granted full use of the observations made there. 
I depended solely on these observations for the height of the barometer. For 
temperature and relative humidity I used an instrument (the polymeter) made by 
LAMBKKUHT, Gottingen. The hygrometer consists of a bundle of human hairs 
mounted in such a way that a pointer is made to move over a very open scale 
showing directly the relative humidity. About once a month the zero was tested by 
painting the hairs with water in the way usual with such instruments. Treated 
in this way the instrument proved quite reliable. A mercury thermometer was 
attached to the metal frame of the hygrometer. The instrument was hung outside 
the window of a porch, the door of which always stood open. In this way the 
thermometer was not influenced by the radiation from a warm room, and. as the 
window looked north, the sun did not shine on it during the day time. The metal 
back of the instrument prevented the thermometer reading too low on a clear evening. 
I had no instrument for measuring the wind strength and had to estimate it as well 
as possible from the "feel." As the wind strength is only used qualitatively, the 
absolute values are of little importance. 



VOL. ccv. A. <> 



[ 99 ] 



IV. The Halogen Hydrides as Conducting Solvents. Part I. The Vapour 
Pressures, Densities, Surface Energies and Viscosities of the Pure Solvents. 
Part II. The Conductivity and Molecular Weights of Dissolved Substances. 
Part III. The Transport Numbers of Certain Dissolved Substances. 
Part IV. The Abnormal Variation of Molecular Conductivity, etc. 

By B. D. STEELE, D.Sc., D. MC!NTOSH, M.A., D.Sc., and E. H. ARCHIBALD, M.A., 

Ph.D. (late 1851 Exhibition Scholars). 

Communicated by Sir WILLIAM RAMSAY, K.C.B., F.lt.S. 
Received February 1, Read February 16, 1905. 



PART I. 

The Vapour Pressures, Densities, Surface Energies and Viscosities of the Pure 
Solvents. By D. MC!NTOSH and B. D. STEELE. 

ALTHOUGH our knowledge of the ionising power of non-aqueous solvents has been 
considerably increased during recent years by the investigations of WALDEN, 
FRANKLIN, KAHLENBERG, and others, the liquefied halogen hydrides and sulphuretted 
hydrogen have received little or no attention. 

GORE (' Phil. Mag.' (4), 29, p. 54), who experimented at ordinary temperatures, 
found that the hydrides of chlorine, bromine, and iodine were very feeble conductors. 
BLECKRODE ('Pog. Ann.' (2), 23, p. 101) stated that hydrogen bromide conducts 
slightly; while HITTORF ('Pog. Ann.' (2), 3, p. 161, 4, p. 374, considered these 
substances to be non-conductors. 

With regard to their behaviour as solvents, SKILLING ('Amer. Ch. Jl.,' 1901, 
26, p. 383) found that at ordinary temperatures sulphuretted hydrogen dissolves 
potassium chloride freely ; but that the solution is a non-conductor of electricity. 

HELBIG and FAUSTI (' Zeit. fur angewandte Chemie,' 1904, 17) state that stannic 
chloride is soluble in hydrogen chloride, but that this solution also is a non-conductor. 

As it seemed highly improbable to us that sulphuretted hydrogen, which is 
analogous to water in so many ways, should be devoid of dissociating power, we 
decided to investigate its solvent action systematically, and at the same time to 
examine the hydrides of chlorine, bromine, iodine, and phosphorus. 

VOL. CCV. A 390. O 2 23.8.05 



100 DR B. D. STEELE, DR. D. McINTOSH AND DE. E. H. ARCHIBALD 

Preliminary Experiments. 

It has been found, as a result of our preliminary experiments, that water and all 
the ordinary metallic salts which were tried are insoluble, or very sparingly soluble, 
in any of the solvents. 

Hydrogen chloride and bromide are freely soluble in hydrogen sulphide, and 
hydrogen sulphide in hydrogen bromide. 

The salts of the organic ammonium bases are soluble in hydrogen chloride, bromide, 
iodide, and sulphide, and the resulting solutions conduct the current. Certain 
ammonium salts also yield very feebly conducting solutions. Two metallic salts, 
namely, sodium acetate and potassium cyanide, were, at first, thought to be soluble, 
as their addition to the solvent greatly increased its conductivity. This has since 
been found to be due to decomposition of these salts into acetic acid and hydrocyanic 
acid respectively. Both of these acids are soluble in the foregoing solvents. 

No substance has yet been found which will dissolve in phosphine and yield a 
conducting solution. 

A few preliminary measurements of the conductivity were made, and in every case 
the molecular conductivity diminished considerably with dilution, instead of increasing 
as it does in aqueous solutions. The results of these measurements are given in 
Part II., which contains a detailed account of the measurements of solubility and of 
conductivity. 

After we had ascertained that the hydrides of chlorine, bromine, iodine, and 
sulphur can act as conducting solvents, we proceeded to the measurement of the 
following physical constants of each of the pure substances : 

(1) The vapour-pressure curve ; 

(2) The density and its temperature coefficient ; 

(3) The surface energy and its temperature coefficient ; 

(4) The viscosity and its temperature coefficient. 

The results of these measurements are described in the following pages. 

Preparation of Liquefied Gases. 

Hydrogen chloride was prepared by the action ol sulphuric acid on pure sodium 
chloride. The gas was dried by passing it through two wash bottles containing 
sulphuric acid, and afterwards through a tube containing phosphoric anhydride. It 
was then led into a receiver which was maintained at -100, by means of carbon 
dioxide and ether, under diminished pressure. At this temperature the gas liquefied 
rapidly, forming a colourless mobile liquid. This was re-distilled before being used 
for the measurements. 



ON THE HALOGEN HYDKIDES AS CONDUCTING SOLVENTS. 101 

The hydrogen bromide was prepared by the action of bromine on red phosphorus 
suspended in water. Traces of bromine were removed by passing the gas through a 
thin paste of amorphous phosphorus and a saturated solution of hydrogen bromide. 
The gas was then dried by passing it over about 40 centims. of phosphoric anhydride, 
and, in order to remove impurities other than water- vapour, it was passed through 
two U-tubes surrounded by solid carbon dioxide, in each of which a small quantity of 
liquefied gas soon collected. The gas bubbled through this liquid, which was thus 
submitted to a process of fractional distillation. It was finally condensed in a vessel 
surrounded by a mixture of carbon dioxide and ether. 

The hydrogen iodide was made by the action of iodine and water on amorphous 
phosphorus, in a similar manner to that employed for the preparation of hydrogen 
bromide, and similar means were used to purify it. The liquid was invariably 
coloured, and it could not be obtained quite colourless even by repeated distillation. 

The hydrogen sulphide was prepared by the action of dilute sulphuric acid on 
ferrous sulphide. The gas was washed by passing it through water, dried by passage 
over phosphoric anhydride, and condensed by means of carbon dioxide and ether. It 
was purified by distillation. 

Phosphuretted hydrogen was prepared by the action of a solution ot potassium 
hydroxide on phosphonium iodide. It was dried by means of phosphoric anhydride 
and condensed in a receiver which was immersed in liquid air. 

The Constant-temperature Bath. 

The constant-temperature bath consisted of ether which was contained in a vacuum 
vessel and cooled by liquid air. The temperature was measured by a constant-volume 
hydrogen thermometer, similar to that described by TRAVERS, SENTER, and JAQUEROD 
('Phil. Trans.,' 1902, A, 200, pp. 105-180). The arrangement of the apparatus is 
shown in fig. 1 , in which C represents the hydrogen thermometer, A the large vacuum 
vessel containing the ether, and B a large vacuum flask containing liquid air. The 
bulb, a, of the thermometer was connected to the dead space of the manometer by a 
fine capillary tube. A mercury reservoir was attached to the stop-cock k by rubber 
tubing, and by raising or lowering this reservoir the mercury in the dead space could 
be adjusted to the level of the glass point c. 

The volume of the thermometer bulb and dead space was carefully determined by 
calibration with mercury. The constants were volume of 

(1) Bulb and portion of stem within the liquid = 17 '480 cub. centims. at ; 

(2) Stem from s to surface of ether = 0'1358 cub. centim. ; 

(3) Dead space and stem to mark s = 0'5719 cub. centim. 

It has been assumed, in making our calculations, that the average temperature of 
the section (2) was midway between that of the bath and that of the atmosphere ; an 
error of a few degrees in the temperature of this section is without influence on the 
bath temperatures, which are given only to the nearest tenth of a degree. 



102 



DE. B. D. STEELE, DK. D. McINTOSH AND DR. E. H. ARCHIBALD 




Fig. 1. 



The vacuum vessel A was closed by a large indiarubber stopper, through which 
holes had been cut to allow the passage of the stem of the thermometer, the apparatus 
containing the liquefied gas, and the tubes I), d, and /. 

The closed tube b was about 7 millims. in diameter and long enough to reach nearly 
to the bottom of the vessel. The tube d was placed so that its open end came 
immediately under the tube b. 

The large vacuum flask B was fitted with tubes as shown in the diagram, so that 
by blowing into / liquid air could be forced into the tube b. 

In order to obtain any desired temperature between that of the room and the 
melting-point of ether ( 117) the vessel A was filled with ether, and the tube d 
connected to an air blast, by means of which the liquid was continuously and 
uniformly stirred, the air escaping through the tube I, which was provided for the 
purpose. 

After mercury had been taken out of the manometer through k, the ether was 
cooled by blowing liquid air from B into b, where it rapidly boiled away. When the 
temperature of the bath had been adjusted, it could be kept constant for as long as 
was desired by blowing liquid air in very small quantities into b. 

The deposition of dew on the walls of the vacuum vessel A was prevented by 
placing it inside a wider cylindrical glass vessel containing phosphoric anhydride. 



ON THE HALOGEN HYDEIDES AS CONDUCTING SOLVENTS. 



103 



Ilie Vapour-pressure, Curves, 

In order to measure the vapour-pressure, a tube containing the liquid was immersed 
in the bath and simultaneous observations of the temperature and corresponding 
vapour-pressure were taken. 

This simple arrangement could not be used with hydrogen bromide and iodide on 
account of the action of these gases on the mercury of the manometer. The errors 
due to this action were avoided by the use of a special 
form of apparatus which is shown in fig. 2. 

To use this apparatus, the tube in was attached to 
the pump, and the bulb a placed in the low-tempe- 
rature bath, after which the whole apparatus was 
exhausted to a pi*essure of about 60 millims. and the 
stop-cock h closed. 

The outer portion of the apparatus was completely 
exhausted and the stop-cock cj closed. A vessel 
containing the liquefied gas was then attached to n by 
rubber tubing, the point I broken within the tube, and 
as soon as a sufficient quantity of liquid had distilled 
into the bulb a the apparatus was sealed off at k. 

Before making any measurements the stop-cock g 
was opened for a few moments, and all traces of air 
were displaced from the tube by allowing a small 
quantity of liquid to evaporate into the pump. 

The bath was cooled to the lowest temperature at 
which observations were to be taken, and the stop- 
cock h opened. As the vapour-pressure of hydrogen 
bromide and of hydrogen iodide, even at the lowest 
temperatures employed, was greater than 60 millims., 
a flow of gas from c into c' followed, and continued until the pressure in the 
manometer became equal to the vapour-pressure of the liquid. As soon as the 
pressure ceased to rise, the temperature and pressure were read and the stop-cock h 
was immediately closed. The temperature was then raised to the next point of 
observation, and the stop-cock h again opened, until the pressure in the manometer 
became constant, when readings were again taken and the stop-cock closed. 

In this way a succession of readings was obtained without the hydrogen generated 
by the action of the gas on the mercury of the manometer finding its way into the 
bulb a. As a precaution against diffusion, the bulbs c, c and the capillary tube e 
were introduced, the stop-cock g being opened after each observation and the 
contents of the bulbs c and c withdrawn through the pump. 




Fig. 2. 



104 DB. B. D. STEELE, DR. D. McINTOSH AND DR. E. H. ARCHIBALD 

The formation of hydrogen was reduced to a minimum by the device of leaving in 
the manometer a small quantity of air, which prevented the hydrogen bromide (or 
iodide) from reaching the surface of the mercury until a considerable time had 
elapsed. 



-60 




ZOO 



400 600 

FffESSURE //V MILLIMETRES OF AfffiCL/ffY 



Fig. 3. 

The results of the measurements are collected in Table I., which contains the 
experimental (a) and smoothed (b) values of the vapour-pressure for each of the 
liquefied gases. 

In the case of hydrogen bromide and iodide the measurements have been continued 
considerably below the melting-point, and the vapour-pressure curve both for solid 
and for liquid are given in fig. 3. It will be noticed that the change in curvature at 
the melting-point is very slight both for hydrogen bromide and for hydrogen iodide. 

The melting- and boiling-points found by us for the pure substances are given in 
Table II., together with recent measurements by other observers. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 

TABLE I. 



105 



Temperature. 


Vapour pressure. 


Temperature. 


Vapour pressure. 


a. 


b. 


a. 


b. 


0. 


miUima. 


millims. 

HYDROGEN 


C. milliins. 

CHLORIDE. 


inillima. 


-80-0 





896 


- 95 


_ 


363 


-80-5 


868 





- 96 





343 


-81 





851 


- 97 





323 


-82 





808 


- 97-2 


31G 





-83 





764 


- 98 





304 


-83-2 


748 





- 99 


. 


287 


-84 


. _ 


718 


-100 





270 


-85 





673 


-101 





254 


-85-9 


648 


. 


-101-3 


245 





-86 





632 


-102 





238 


-87 





594 


-103 





225 


-88 





557 


-104 





210 


-89 





552 


-104-5 


198 





-89-8 


522 





-105 





19G 


-90 





493 


-'106 





184 


-91 


. 


463 


-107 





173 


-92 





435 


-108 





102 


-92-9 


430 





-109 





149 


-93 





410 


-109-9 


141 





-94 





385 


-110 


138 


HYDROGEN IODIDE. 


-35 


_ 


783 - 56 





274 


-35-9 


769 


- 57 





258 


-36 





750 - 58 





244 


-36-9 


713 





- 59 





230 


-37 





718 


- 59-5 


224 





-38 





686 


- 60 





218 


-39 





657 


- 61 





206 


-39-4 


644 





- 62 





194 


-40 





628 


- 63 





183 


-41 





600 


- 63-5 


185 





-41-7 


578 





- 64 





173 


-42 





573 


- 65 





162 


-43 





547 


- 66 





152 


-43-5 


530 





- 67 





143 


-44 





519 


- 68 





134 


-45 





494 


- 68-4 


126 





-46 





471 


- 69 





126 


-47 





448 


- 70 





118 


-47-7 


438 





- 71 





111 


-48 





425 


- 72 





103 


-49 


. 


404 


73 





97 


-50 


376 


. . 


- 73-5 


92 





-51 





364 


- 74 





90 


-52 





343 


- 75 





84 


-53 





325 


- 76 





79 


-54 





307 


- 77 





73 


-54-8 


303 





- 77-9 


74 


. 


-55 




289 - 78 





70 



VOL. CCV. A. 



106 



DE. B. D. STEELE, DR. D. McINTOSH AND DE. E. H. AECHIBALD 



TABLE I. (continued). 



Temperature. 


Vapour pressure. 


Temperature. 


Vapour pressure. 


a. 


6. 


a. 


b. 


c. 


milliiiis. 


millims. " C. millims. 

HYDROGEN BROMIDE. 


millims. 


-65 








- 87 


_ 


283 


-66 





891 


- 87-1 


284 





-67 





835 


- 88 


266 


-68 





785 


- 89 





259 


-68-4 


775 





- 89-3 


245 




-69 





743 


- 90 





247 


-70 





704 


- 91 


239 


-70-7 


682 





- 92 


222 


-71 





671 


- 92-8 


214 




-72 





635 


- 93 




214 


-73 


609 


- 94 





204 


-74 


575 





- 95 





195 


-75 





546 


- 96 





187 


-76 





519 


- 96-3 


185 




-76-7 


501 





- 97 




177 


-77 





483 


- 98 





167 


-78 





468 


- 99 





157 


-79 





445 


-100 





147 


-79-3 


431-5 





-100-7 


142 




-SO 





423 


-101 




136 


-81 





402 


-102 





125 


-82 





381 


-103 





114 


-83 


357 





-104 





102 


-84 





340 


-104-2 


96 




-85 





321 


-105 




90 


-86 


~ 


302 








SULPHURETTED HYDROGEN. 


-60 





770 


- 74 




345 


- 61 

n f* 





724 


- 75 





326 


- 62 





682 


- 75-6 


314 




-62-2 


676 





- 76 




309 


- 63 





644 


- 77 





292 


-64 





607 


- 78 





276 


- 65 





573 


- 78-4 


270 




- 66 
-66-1 

nrj 


538 


541 


- 79 
- 80 




261 
246 


- 67 
-68 

C(\ 





513 

484 


- 81 
- 81-7 


220 


232 


69 
-69-1 

-70 

n" 


456 


458 
432 


- 82 
- 83 
- 84 


193 


218 
205 


-71-6 

*7O 


400 


409 


- 85 
- 86 





181 
169 


IZ 

-73 





384 
364 


- 87 
- 88 





158 
148 



ON THE HALOGEN HYDKIDES AS CONDUCTING SOLVENTS. 



107 



TABLE I. (continued). 





Vapour pressure. 




Vapour pressure. 


Temperature. 




Temperature. 














a. 


b. 




a. 


b. 


C. 


million. 


ruillinis. 

PHOSPHURETT 


C. 
ED HYDROGEN. 


millims. 


millims. 


-86 





770 


- 97 





403 


-86-6 


719 





- 97-7 


393 





-87 


. 


716 


- 98 





382 


-88 





668 


- 99 





362 


-88-6 


644 





-100 





342 


-89 





630 


-101 





324 


-90 





595 


-101-2 


319 





-91 


. 


563 


-102 





305 


-92 





531 


-103 





287 


-93 





503 


-104 





269 


-93-1 


498 





-105 





253 


-94 





473 


-105-9 


237 





-95 





448 


-106 





235 


-96 





425 










1 













TABLE 


II. 








HCl. 


HBr. 




H,S. 


PH S . 


r 

Melting-point< I 
l 


-111-1 
-111-3 


-86 
-88-5 
-86-1 


-50-8 
-50-8 
-51-5 


-82-9 





f* 

Boiling-point < I 

L 


- 82-9 
- 83-7 
- 83-1 


-68-7 
-64-9 
-68-1 


-35-7 
34-1 
36-7 


-60-2 
60-4 


86-4 
-85 



* MclNTOSH and STEELE. 

t ESTREICHER, ' Zeit. Phys. Chem.,' 1896, 20, p. 605. 
J LADENBERG and KRUGEL, ' B. B.,' 1900, 33, p. 637. 
OLSZEWSKI, ' Monatshefte fiir Chemie,' 7, p. 371. 



Heats of Evaporation. 

CLAUSIUS has shown that the heat of vaporisation of a liquid can be calculated 

from the equation 

dp ^ 

~~ 



^ 

dT ~~ KT 2 ' 
p 2 



108 



DE. B. D. STEELE, DE. D. McINTOSH AND DE. E. H. AECHIBALD 



TO PUMP 



in which - P - represents the change of vapour-pressure with temperature, P the 

(/ A 

pressure, T the absolute temperature, R the constant of the gas equation, and W the 
latent heat of evaporation of one gram-molecule of the liquid. 

The values of W at a pressure of 760 millims., as calculated from our vapour- 
pressure curves, are 

for hydrogen chloride, 14'8 x 10 10 ergs, 

bromide, 17'4xl0 10 

iodide, 207 xlO 10 

sulphide, 19'3xl0 10 

phosphuretted hydrogen, 17 '2 x 10 10 ,, 

We can find no account of any direct determination of W for these substances. 

The Measurement of Density. 

The apparatus (fig. 4) employed for these measurements consisted of a bulb with a 
graduated capillary stem, to which a two-way stop-cock c was attached. 

The bulb had a capacity of about 1*5 cub. centim., and 
its volume and that of each division of the stem was 
accurately determined by calibration with mercury. After 
the tube a had been sealed to the pump, and the apparatus 
exhausted, it was immersed in the constant-temperature 
bath. The tube b was then connected to a vessel con- 
taining the liquefied gas, which was distilled into the bulb 
until both bulb and stem were completely filled. The 
stop-cock was turned and the liquid allowed to evaporate 
into the pump until the meniscus had come to a definite 
position on the stem, when the stop-cock was turned so 
as to disconnect all the tubes. To obtain the volumes 
occupied by a constant weight of liquid, it was only 
necessary to read the position of the meniscus at different 
temperatures. 

The weight of liquid was obtained by attaching to the 
Fig. 4. tube b a weighed set of GEISSLER'S bulbs containing 

potassium hydrate solution. 

On opening the stop-cock and raising the temperature of the bath the liquid 
evaporated and the gas was absorbed in the bulbs and weighed. 

To prevent the potash solution sucking back, a little mercury was placed in the 
first bulb. The small amount of gas remaining in the apparatus was finally pumped 
out through a and measured. 




<i 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 



109 



The numbers obtained by the foregoing method have been checked in the case of 
hydrogen chloride, hydrogen bromide, and hydrogen iodide by distilling each of them 
into a thick-walled bulb of known volume, and sealing it. After the bulb containing 
the liquid had been weighed it was cooled, the stem broken, and the empty bulb and 
stem again weighed. 

The densities so obtained agreed to the 3rd decimal place with those obtained at 
the same temperature by the first method. 

In the case of phosphine the density was determined by the second method and the 
temperature coefficient by the first method. 

The results of the measurements are given in Table III., in which D' represents 
the experimental and D the smoothed value of the density. The density in each case 
is a linear function of the temperature and is given by the relation 

D T , = D T [l + a(T-T')], 

where T and T' represent the boiling-point and the temperature of observation 
respectively, both on the absolute scale ; D T and D T , being the corresponding 
densities. 

The values of the coefficient a for the different substances are contained in the 
following table : 



HC1 


D r = 1-187 


1+ 000268 (T-T')] 


HBr 


D T - = 2-157 


1+0-0041 (T-T') 


' HI D T . =2-799 


1+0-0043 (T-T') 


H.,S D r = 964 


'1+0-00109 (T-T') 


PH 3 


D r =0-744 


1+0-0008 (T-T')" 



TABLE III. Densities. 



T (jibs.). 


D. 


D'. 


T (abs.). 


I). 


D. 


"aba. 


1 


abs. 








HYDROGEN CHLORIDE. 


164-0 


1-257 180 1-213 





166 


1-251 





180-1 


1-2127 


168 


1-246 


. 


182 


1-207 





168-5 





1-2438 


183-2 





1-2038 


170 


1-240 





184 


1-201 





171-8 





1-2347 


186 


1-196 





172 


1-234 





187-2 





1-1937 


174 


1-229 





188 


1-190 





175-8 


. 


1-2242 


189-9 





1-1842 


176 


1-224 





190 


1-185 





178 


1-218 





192 


1-179 






110 DR. B. D. STEELE, DK. D. McINTOSH AND DK. E. H. ARCHIBALD 

TABLE II L Densities (continued). 



T (abs.). 


D. 


D'. 


T (abs.). 


D. 


D'. 


abs. 






"abs. 






HYDROGEN BROMIDE. 


182 


2-245 


_ 


195-3 


2-1932 


184 


2-237 





196 


2-191 





184-7 




2-2337 


198 


2-183 





180-0 





2-2286 


198-2 





2-1823 


186 


2-229 





200 


2-176 





188 


2-222 


. 


200-4 





2-1742 


190 


2-214 





202 


2-168 





192 


2-206 





203-8 





2-1600 


193-3 




2-2047 


204 


2-160 





194 


2-199 











HYDROGEN IODIDE. 


222 


2-863 




232 2-822 





223-3 





2-8600 


232-9 


2-819 


224 


2-855 





234 


2-813 





224-9 





2-8496 


236 


2-805 





'226 


2-847 





236-3 





2-8034 


227-0 





2-8412 


238 


2-796 





228 


2-838 





240 


2-787 





229-3 





2-8330 


240-4 





2-7862 


230 


2-830 





242 


2-779 





HYDROGEN SULPHIDE. 


190 1-004 




201-5 


0-9846 


191-3 


1-0019 


202 


0-984 





192 


1-001 


. 


203-9 





0-9806 


194 


0-998 





204 


0-980 





194-6 


0-9968 


206 


0-976 





196 0-994 





206-9 





0-9759 


197-4 





0-9925 


208 


0-973 





198 


0-991 





210 


0-970 





199-7 





0-9875 


210-8 





0-9692 


200 


0-987 





212 


0-967 





PHOSPHURETTED HYDROGEN. 


166 


0-761 


_ 


180 


0-750 





167-1 





0-7604 


182 


0-748 





168 


0-760 





184 


0-747 





170 


0-758 





184-4 





0-7465 


171-8 





0-7560 


186 


0-745 


. 


172 


0-756 





186-5 





0-7448 


174 


0-755 





188 


0-743 


. 


175 





0-7534 


190 


0-742 





176 


0-753 





192 


0-740 





178 


0-751 





192-8 





0-7392 


179-9 





0-7504 


194 


0-739 






ON THE HALOGEN HYDKIDES AS CONDUCTING SOLVENTS. 



Ill 



KOPP has shown that the molecular volume of a liquid at its boiling-point is an 
additive property, being equal to the sum of the atomic volumes of the component 
elements. Certain elements, however, such as oxygen, appear to possess two values 
for the atomic volume, depending on the nature of the linking of the oxygen to the 
other atoms in the molecule. 

It has also been shown that, in the case of the elements chlorine, bromine, and 
sulphur, the atomic volumes calculated from the density of compounds containing 
them are the same as those obtained from the densities of the pure elements. We 
have calculated the atomic volumes of the elements chlorine, bromine, iodine, sulphur, 
and phosphorus from the densities of their respective hydrides, in order to see how 
the values so obtained agree with those given by KOPP and others. 

The results of these calculations are given in Table IV., which contains D, the 
densities of the compounds at their respective boiling-points, the molecular volume 
M/D, and the atomic volume A' of the halogen elements. 

The values of these are invariably higher than those of KOPP, which are given 
under A, in the fifth column. It is possible that this discrepancy is due to a variation 
in the atomic volume of hydrogen, which has accordingly been calculated from each 
compound by subtracting the figures in the fifth column from those in the third. 

The values for A, so obtained, are given in the last column, and are uniformly 
higher than 5 '5, which is the number found from the study of organic compounds. 

TABLE IV. Molecular Volumes at Boiling-point. 



Substance. 


D. 


M/D. 


A'. 


A, KOPP, &c. 


AA. 


HC1. . . . 
HBr . . . 


1-185 
2-158 


30-8 
37-4 


25-3 
31-9 


22-8 
27-9 


8-0 
9-5 


HI . 


2-799 


45-7 


40-2 


37-8 


7-9 


H,S 


0-964 


35-2 


24-2 


22 -G 


6-3 


H 3 P . . . 


0-743 


45-7 


29-2 


/21-9* 


8-0 










\2C-Ot 


6-6 



* MASSON. t THORPE. 



The Molecular Surface Energies. 

The molecular surface energies were measured by RAMSAY and SHIELDS' method, 
slightly modified in order that the measurements might -be made at low temperatures. 
The apparatus (fig. 5) consisted of a tube b, 6 centims. long and 1'3 centims. in 
diameter, which was provided with a small side tube d, and joined to a two-way 
stop-cock by a long tube a. 

A small glass scale s, which had been very carefully calibrated, was securely fixed 
inside b. The capillary c was sealed to a long tube g, in the manner described by 



112 



DR. B. D. STEELE, DR. D. McINTOSH AND DR. E. H. ARCHIBALD 



RAMSAY and SHIELDS. The tubeg, which enclosed a piece of soft iron, i, was selected 
so as to slide easily and smoothly in a. It was held in position by the two glass 
hooks e and /, which were placed so that when / was resting on e the bottom of the 
capillary was a few millimetres below the scale. 



TO PUMP 




Fig. 5. 

A mark had been previously etched on the capillary, and when making the 
measurements the position of the tube g was adjusted by means of an electro-magnet, 
so that this mark always coincided with the meniscus inside the capillary. The 
radius of the capillary near the etched mark was determined by introducing a 
quantity of pure ether into the apparatus, and measuring the height of the column of 
liquid when the capillary was in different positions. The radius could then be 
calculated from KAMSAY and SHIELDS' values for the surface energy of ether. The 
following values were found : 



Position of meniscus. 


Height of ether column. 


Radius. 


At the mark 


millims. 

34-28 


013767 


1 9 millims. below mark . . 

0-4 
u * 

1 1 above . . 

7 >F i 
1 u j 


34-29 
34-32 
34-31 
34-57 


013763 
013751 
013755 
013652 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 



113 



To carry out the experiments, the apparatus was placed in the constant-temperature 
bath and exhausted through the tube L The stop-cock h was then turned, and an 
excess of the liquid to be measured was introduced through the tube I by distillation. 
The stop-cock was again turned, and all traces of air were displaced from the apparatus 
by allowing some of the liquid to evaporate into the pump, after which the stop-cock 
was closed. The bath was then maintained successively at different temperatures, 
and the mark on the capillary having first been brought into coincidence with the 
meniscus, the height of the column of liquid was accurately measured. 

The tube d was attached to a manometer, and measurements of the vapour-pressure 
of the liquid were made during the experiment. This tube was removed during the 
measurements of hydrogen bromide and hydrogen iodide. 

The results of the measurements are given in Tables V. to IX., in which the letters 
employed have the following meaning : 

T = the absolute temperature ; 
D = the density of the liquid ; 
(T = the density of the vapour ; 
V = the specific volume of the liquid ; 
V.P. = the vapour-pressure of the liquid ; 

h = the height of the column of the liquid ; 
y = surface tension in dynes per centimetre = J ryh (D er) ; 
y (MV) 3 = the molecular surface energy in ergs ; 
g = the constant of gravity ; 
M = the molecular weight of the liquid. 



TABLE V. Hydrochloric Acid. 



T (abs.). 


D. 


<T. 


D-ov 


V.P. 


h. 


y- 


(MV)i. 


y(MV)>. 


163-1. 


[1-2530] 


0-00051 


1-2525 


miHims. 

141 


centime. 

3-303 


27-874 


9-4600 


263-68 


168-5 


1-2438 


0-00069 1-2431 


198 


3-214 


26-912 


9-5073 


255-87 


171-7 


1-2347 


0-00083 


1-2339 


245 


3-152 


26-251 


9-5537 


250-80 


175-8 


1-2242 


0-00105 


1-2232 


316 


3-094 


25-477 


9-6080 


244-78 


180-1 


1-2127 


0-00139 


1-2113 


430 


3-033 


24-718 


9-6690 


239-00 


183-2 


1-2038 


0-00167 


1-2021 


522 


2-974 


24-046 


9-7167 


233-65 


187-2 


1-1937 


0-00202 


1-1917 


648 


2-936 


23-467 


9-7725 


229-30 


189-9 


1-1842 


0-00230 


1-1819 


748 


2-866 


22-760 


9-8233 


223-57 


192-6 


1-1770 


0-00263 


1-1744 


868 


2-838 


22-409 


9-8634 


221-03 



VOL. CCV. A. 



114 



DE. B. D. STEELE, DR. D. McINTOSH AND DR, E. H. ARCHIBALD 
TABLE VI. Hydrobromic Acid. 



T (abs.). 


D. 


<T. 


D-o-. 


V.P. 


k. 


y. (MV)I. 


y(MV)I. 


181-8 
184-7 
186-1 
188-9 
193-4 
195-3 
198-2 
200-5 
203-9 


[2-2400] 
2-2337 
2-2286 
[2-2185] 
2-2047 
2-1932 
2-1823 
2-1742 
2-1600 


0-0015 
0-0018 
0-0019 
0-0023 
0-0028 
0-0031 
0-0035 
0-0039 
0-0047 


2-2385 
2-2319 
2-2267 
2-2158 
2-2019 
2-1901 
2-1788 
2-1703 
2-1553 


millims. 
210 

250 
275 
327 
410 
430 
525 
600 
730 


centims. 

2-015 
1-990 
1-958 
1-926 
1-887 
1-830 
1-800 
1-790 
1-740 


30-191 10-932 
29-728 10-953 
29-182 10-970 
28-570 11-014 
27-812 11-049 
27-019 11-087 
26-440 11-124 
26-201 11-152 
25-399 11-201 


330-1 
325-6 
320-1 
314-6 
307 30 
299-6 
294-8 
292-2 
284-5 



TABLE VII. Hydriodic Acid. 



T (abs.). 


D. 


<T. 


D-cr. 


225-3 


2-8523 


0-0039 


2-849 


227-1 


2-8401 


0-0042 


2 836 


229-3 


2-835 


0-0045 


2-831 


230 9 


2-829 


0-0048 


2-824 


232-9 


2-820 


0053 


2-815 


235-0 


2-812 


0-0057 


2-806 


236-5 


2-806 


0-0061 


2-800 



V.P. 


h. 


' 


(MY),. 


y( MV), 


inillims. 

420 


centims. 

1-511 


29-06 


12-63 


367-0 


460 


1-496 


28-64 


12-67 


362-8 


503 


1-479 


28-26 12-69 


358-6 


558 


1-467 


27-97 12-71 


355-5 


595 


1-451 


27-57 


12-73 


351-0 


655 


1-440 


27-27 


12-76 


348-0 


700 


1-427 


26-96 


12-78 


344-6 



TABLE VIII. Sulphuretted Hydrogen. 



T (abs.). 


D. 


IT. 


D-o-. 


V.P. 


h. 


y- 


(MV)i 


y (MV)i. 


189-0 


[1-006] 


0-00055 


1-006 


millims. 

192 


centims. 

4-962 


33-418 


10-458 


349-5 


191-3 


1-002 


0-00063 


1-001 


219 ! 4-906 


32-902 10-495 


345-3 


194-6 


0-997 


0-00076 


0-996 


269 


4-816 


32-126 10-522 


338-0 


197-4 


0-992 


0-00086 


0-992 


313 


4-765 


31-645 10-557 


334-1 


199-7 


0-987 


0-00098 


0-986 


363 


4-695 


31-020 10-584 


328-3 


201-5 


0-985 


0-00107 


0-984 


399 


4-676 


30-813 10-604 


326-6 


203-9 


0-9806 


0-00122 


0-979 


454 I 4-642 


30-448 


10-639 


324-7 


206-9 


0-9759 


0-00142 


0-975 


536 4-540 


29-631 10-669 


316-7 


210-8 


0-9692 


0-00175 


0-968 


674 


4-442 


28-783 10-720 


308-6 



TABLE IX. Phosphuretted Hydrogen. 



















T (abs.). 


D. 


or. 


D-o-. 


V.P. 


h. 


y- 


(MV)5. 


y(MV)', 


167-1 


0-760 


0-00079 


0-7592 


millims. 

237 


centims. 

4-484 


22-783 


12-605 


287-2 


171-8 


0-756 


0-00101 


0-7550 


319 


4-372 


22-095 


12-654 


279-6 


175-4 


0-753 


0-00122 


0-7522 


393 


4-282 


21-553 


12-683 


273-4 


179-9 


0-746 


0-00151 


0-7450 


498 


4-171 


20-798 


12-761 


265-4 



ON THE HALOGEN HYDKIDES AS CONDUCTING SOLVENTS. 



115 



The foregoing results are represented graphically in fig. 6, in which the molecular 
surface energies are plotted against the absolute temperature. 



^200 



180 



170 



160 



200 



\ 



,^> 



^ 



250 300 

MOLECULAR SURFACE ENERGY 

Fig. 6. 



350 



EF?GS. 



The range of temperature over which measurements were made was small, and in 
the case of each substance the curve appears to be a straight line. 



d 



The temperature coefficients -j- y (MV) ?i are given in Table X. 



dt 



TABLE X. 



Q 2 



Substance. 


Temperature range. 


| y( MV)I. 


Hydrogen iodide. . . . 
bromide . . . 


225-236 
181-204 


1-99 
2-03 


sulphide . . . 
phosphide . . 
chloride . . . 


189-211 
167-180 
159-192 


1-91 
1-70 
1-47 



116 DE. B. D. STEELE, DR. D. McINTOSH AND DK. E. H. AECHIBALD 

The average value of this coefficient is, according to EOTVOS, 2'27. From the 
experiments of RAMSAY and SHIELDS it is 2-12, while BALY and DONNAN have found 
that the liquefied gases oxygen, nitrogen and carbon monoxide give values very near 
to 2, and this number has also been found by us for the three substances hydrogen 

bromide, iodide and sulphide. 

RAMSAY and SHIELDS have shown that for normal liquids the relation between 
molecular surface energy and temperature is given by the equation 



in which t represents the temperature measured from the critical point and d is a 

small constant. 

From this equation it follows that the surface energy disappears at a temperature 
d degrees below the critical point, and therefore the curve for a normal liquid, if 
produced, should cut the temperature axis at this point. 

This is the case for hydrogen bromide, iodide and sulphide, for which, as will be 
seen from Table XL, the value of d is 16'3, 157 and 0'2 respectively. 



HI-* 
400 

/y g j-> 

HB^ 

I 

5300 

I 

?00 

180 










































*v 










































"X 


x. 




































\ 








\ 


\ 


































"\ 


X. 






"\ 


-v. 




























V. 


^ 




\ 


N 






' Xfc - 


s. 



































^ 


% 






X 


^ 




























V. 


^ 




*S* 


\ 






" J 


. 




























% 


' V 


, 


N. 


^ 






" -N 


v 






























"^ 


t<5> 


NS 


x 






x 


^ 






























X 




^^ 


x 






^>v 


v. 
































"\ 

"V, 


Vs, 


^, 






































Vs 


^^ 








) 100 200 300 40 



ENERGY 



Fig. 7. 



The curves are shown in fig. 7, in which the critical temperature of each liquid is 
indicated by an arrow. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 

TABLE XL 



117 





Critical temp. 


Temp, at which 
curve cuts T axis. 


d. 


Hydrogen chloride 
,, bromide 


0. 
52-3 
91-3 


"0. 

65-2 
75-0 


+ 11-9 
16-3 


,, iodide 


150-7 


134-0 


15-7 


,, sulphide 


100-2 


100 -0 


- 0-2 


Phosphuretted hydrogen . . . 




61-6 





RAMSAY and SHIELDS also showed that another class of liquid exists, for which the 
above relation does not hold, inasmuch as the coefficient not only was less than 2 '12, 
but also varied with the temperature. If a tangent is drawn to the curve, for a 
liquid of this class, it will cut the temperature axis at a point above the critical 
temperature. 

This abnormal behaviour is explained by the assumption that the molecules of such 
liquids are associated to form larger molecular complexes ; in other words, that their 
molecular weights are abnormally high. Hydrogen chloride and phosphide, from the 
magnitude of their temperature coefficients, must be classed with the abnormal or 
associated liquids, but the curves which we have obtained are too short to be 
distinguished from straight lines. These curves have, however, been produced and 
the results are shown in fig. 8 and Table XI. 



x>v 

330 


x 




































V 






























71ft 




_^ 


\ 




























?on 






X " 


v. ^ v 


































X, 




^ 






















270 










X 


>v 




















^ 












X ^ 
































s. 


^ x 


















^ 
k 














' 


^ 


















V 


?50 
































$ 














\ 
































N, 


















u. 


30 
















X 
















k^ 
































?f\(\ 


















X 


X. 


*x 
































X 

x 




X. 
X. 

X, 










iyo 

i7n 
























\ 




\ 






i/U 

150 


























N 


N 






> 


40 


60 


l?0 160 200 ZW 2BO 



MOL SURFACE ENERGY. 
Fig. 8. 



118 

It will 
65-2, or 



measured 
at 22. 
In the 



DR. B. D. STEELE, DR. D. McINTOSH AND DR. E. H. ARCHIBALD 

be seen that the curve for hydrogen chloride cuts the temperature axis at 

11-9 above the critical point. 

We have not been able to find any record 
of measurements of the critical temperature of 
phosphuretted hydrogen. 

The Measurement of Viscosity. 

The viscosity apparatus (fig. 9) was of the 
usual form, but with some slight additions, 
which were designed to prevent access of water 
vapour. For this purpose the two ends of the 
apparatus were joined to the stop-cock h, and 
the two tubes c and d, containing phosphoric 
anhydride, were attached. After the apparatus 
had been placed in the bath, a definite quantity 
of the liquid was distilled into it through d. 

In order to make the measurements, the stop- 
cock was closed and, by blowing into d, the 
liquid was forced into f until it reached a 
position about one centimetre above the mark a. 
The stop-cock was then opened and the time 
required for the liquid to fall from a to b 
with a stop-watch. The apparatus was calibrated with distilled water 




tables, D refers to the density of the liquefied gas; 17 is the viscosity 

compared with that of water at 22, and -3- is the temperature coefficient of viscosity. 

ctt 



TABLE XII. Hydrogen Chloride. 
Apparatus B. Time of flow for water = 7 5 '3 seconds at 22. 













1 


T (abs.). 


Time. 


D. 


*? 


dr, 

dt ' 


Smoothed -2 . 
dt 










per cent. 


per cent. 


160-8 


35-1 


1-265 


0-590 








166-7 


34-3 


1-249 


0-569 


0-61 





171-7 


32-3 


1-236 


0-530 


0-03 





177-0 


31-7 


1-221 


0-514 


0-91 





183-2 


30-8 


1-204 


0-493 


0-88 





188-2 


30-2 


1-189 


0-477 


0-86 


0-88 



ON THE HALOGEN HYDWDES AS CONDUCTING SOLVENTS. 



119 



TABLE XIII. Hydrogen Bromide. Apparatus B. 



T (abs.). 


Time. 


D. 


'/ 


dt\ 

~di' 


Smoothed -^ . 
dt 


186-8 


30-8 


2-227 


0-911 


per cent. 


per cent. 


188-8 


30-6 2-219 


0-902 


0-50 





190-8 


30-3 2-212 


0-890 


0-59 





193-7 


30-0 


2-200 


0-877 


0-57 





197-3 


29-5 


2-186 


0-857 


0-60 





199-4 


29-4 


2-178 


0-851 


0-56 


0-57 



TABLE XIV. Hydrogen Sulphide. Apparatus B. 











1 


T (abs.). 


Time. 


D. 


* 


~ctt ' 


Smoothed "H . 
dt 






per cent. 


per cent. 


191-0 


40-3 


1-002 0-547 


_ 


193-3 


39-8 


0-998 0-528 


1-6 




198-2 


38-8 0-990 0-510 


1-0 





201-2 


37-3 0-985 0-488 


1-19 


_ 


206-1 


36-2 0-977 0-470 


1-09 





209-8 


35-2 0-972 


0-454 


1-08 


1-1 



TABLE XV. Hydrogen Iodide. Apparatus A. Time of flow for Water = 43 seconds 

at 22. 



T (abs.). 


Time. 


D. 


,. 


dt' 


Mean. 






1 


per cent. 


per cent. 


223-3 


22-3 


2-858 


1-479 








225-6 


22-0 


2-849 


1-454 


0-75 





227'2 


21-8 


2-842 1-437 


0-75 





229-6 


21-7 


2-832 


1-426 


0-59 





231-5 


21-4 


2-824 


1-402 


0-67 





233-9 


21-1 


2-813 


1-377 


0-70 





236-4 


20-8 


2-802 


1-353 


0-71 


0-70 


SUMMARY of Tables XII. to XV. 








dn 






Substance. 


>! at B.P. 


dt ' 






HC1 


0-47 


0-90 






HBr 


0-83 


0-58 






HI 


1-35 


0-70 








H 2 S . . 


0-45 


1-10 







120 



DE. B. D. STEELE, DR. D. McINTOSH AND DK. E. H. ARCHIBALD 



PAET II. 



Tli e Conductivity and Molecular Weights of Dissolved Substances. 

and E. H. AKCHIBALD. 



By D. MCINTOSH 



THE second part of this investigation deals with the solubilities of substances in the 
liquefied halogen hydrides and sulphuretted hydrogen, and with the conductivities of 
the resulting solutions ; the molecular weights of a few substances, when dissolved in 
each of these solvents, have also been determined. 



The Temperature Bath. 

As liquid air was not available in sufficient quantities to make use of the bath 
described in Part I., a mixture of carbon dioxide and ether, which under atmospheric 
pressure gives a very constant temperature of 81, was used for the measurements of 
solutions in hydrogen bromide and sulphide. 

The same mixture, under reduced pressure, was used for the measurement of 
solutions in hydrogen chloride. By carefully regulating the pressure over the 
mixture the temperature was maintained at 100. 

For the hydrogen iodide solutions a temperature of 50 was 
obtained by slowly running cold ether into the vacuum vessel 
and syphoning off the warmer upper layer. 



The Determination of Solubilities. 

The solubilities were measured by means of an apparatus 
(fig. 1) which consisted of a test-tube A, to the bottom of which 
a delivery tube B was sealed. The bottom of A was covered 
with a thick layer of asbestos which acted as a filter, and the 
whole was immersed in the constant-temperature bath. 

The liquefied gas and the substance of which the solubility was 
under investigation were introduced into A, where they were 
vigorously stirred with a platinum rod. A portion of the liquid 
was then blown through the delivery tube into a weighed and 

The volume of liquid in the test-tube was observed, the liquid 




Fig. 1. 



graduated test-tube. 

allowed to evaporate, and the residue weighed. The solubility was calculated from 

the data thus obtained. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 121 

The results of the measurements may be summarised as follows : 

(1) Inorganic substances insoluble, or soluble only in traces, in any of the 
solvents 

The chlorides, bromides, and iodides of the alkalis and alkaline earths : salts 
of -nickel, iron, lead, and mercury ; stannous chloride, potassium 
permanganate, and potassium bichromate. 

(2) Inorganic substances soluble in some cases with decomposition : 

(a) In hydrogen chloride 

*Stannic chloride, phosphorus pentabromide, phosphorus pentachloride, 
and phosphorus oxychloride ; 

(b) In hydrogen bromide 

Phosphorus oxychloride, bromide, and sulphuretted hydrogen ; 

(c) In hydrogen iodide- 

Iodine and phosphorus oxychloride ; 

(d) In sulphuretted hydrogen 

Sulphur, phosphorus oxychloride, hydrogen bromide, and hydrogen 
chloride. 

(3 ) Inorganic substances soluble with decomposition in hydrogen chloride, potassium 
cyanide, ammonium sulpho-cyanate, sodium acetate. 

(4) Organic substances. In addition to the organic ammonium bases, which, as 
stated in Part I., dissolve somewhat freely in all the solvents, we have found that a 
very large number of organic compounds are soluble, as, for example, the aldehydes, 
ketones, alcohols, ethereal salts of fatty and of aromatic acids, cyanides, and sulpho- 
cyanates, hydrocarbons, and nitro-compounds. Hydrogen sulphide is an excellent 
solvent for such bodies, but the solutions, as a rule, are non-conductors. The solutions 
hi the halogen hydrides, on the other hand, usually conduct the current. 

77; e Measurement of Conductivity. 

Although the investigation of the solubility of inorganic salts failed to indicate that 
these were soluble in more than traces in any of the solvents, we have tested the 
conductivity of the different solvents after the addition of certain inorganic substances. 
We find that an increase of conductivity was produced by adding the following 
substances to : 

* HELBIG and FAUSTI ('Atti E. Accad. Lincei,' 1904 (V), 13, p. 30) found that stannic chloride was 
soluble in hydrogen chloride. We regret that by an oversight we contradicted this statement in our 
Preliminary Note ('Roy. Soc. Proc.,' 1904, 73, p. 554), and we wish now to make the necessary correction. 

VOL. CCV. A. R 



122 DR. B. D. STEELE, DR. D. McINTOSH AND DR. E H. ARCHIBALD 

(a) Hydrogen chloride 

Bromine, potassium iodide, thionyl chloride, sulphuryl chloride, and 
uranium nitrate (very slight increase), phosphorus pentachloride, 
pentabromide, and oxychloride (considerable increase) ; 

(b) Hydrogen bromide 

Phosphorus oxychloride (considerable increase) ; 

(c) Hydrogen iodide- 

Iodine, sulphuric acid, carbon disulphide, and phosphorus oxychloride 
(slight increase) ; 

(d) Sulphuretted hydrogen- 

Phosphorus pentachloride, and sulphuryl chloride (slight increase). 

The following substances did not cause an increase in the conductivity of either of 
the solvents : 

Sodium, sodium sulphide, sodium biborate, sodium acid phosphate, sodium nitrate, 
sodium sulphide, sodium thiosulphate, sodium arsenate, chromic acid, the following 
salts of potassium : the nitrate, hydroxide, chromate, sulphide, acid sulphate, 
ferrocyanide, ferricyanide ; ammonium fluoride and carbonate ; rubidium and caesium 
chlorides ; 

Magnesium sulphate, calcium fluoride, strontium chloride, barium chloride, oxide, 
nitrate and chromate ; copper sulphate, mercuric chloride, zinc sulphate, boron 
trichloride, aluminium chloride, and sulphate ; carbon dioxide, stannous chloride, lead 
peroxide, nitrate, and cyanide ; phosphorus tribromide, bismuth nitrate, tartar emetic, 
manganese chloride, ferric chloride, ferrous sulphate, nickel sulphate, and cadmium 
sulphate. 

In addition to the organic ammonium bases, we have, in conjunction with 
Dr. J. W. WALKER,* examined the conductivity of solutions of about 80 organic 
substances in each of the foregoing solvents. 

The only substances which form conducting solutions in H 2 S are the ammonium 
bases and a few alkaloids such as nicotine and pyridine. On the other hand, many 
ethers, ketones, esters, nitrites, and, generally speaking, substances containing oxygen 
or nitrogen, form conducting solutions in hydrogen chloride, bromide, and iodide. 
The hydrocarbons, although in some cases soluble in all proportions, do not conduct. 
We have noticed that the solution of those substances which conduct is accompanied 
by a considerable evolution of heat, while little or no heat is evolved in the case of 
other substances. 

This indicates chemical interaction between the conducting solute and the solvent, 
and many of the resulting compounds have been isolated and analysed.! It has been 

* 'Journal of the Chemical Society,' 1904, 85, p. 1098. 
t ARCHIBALD and MC!NTOSH, ' J. C. S.,' 1904, 85, p. 919. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 



123 



found, for example, that ether enters into combination with the three halogen acids, 
forming compounds which have the following formulae : 

(C 3 H 5 ) 2 0, 5HC1, M.P. = -120, 
(C 3 H 5 ) 2 0, HBr, M.P. = - 42, 
(C 2 H 5 ) 2 O, HI, M.P. = - 18. 

We have explained the formation of these and similar compounds by assuming the 
existence of tetrad oxygen at these low temperatures. 

The compound of ether and hydrogen bromide would thus have the formula 

p 2 Tj /O\r>,> an d might be expected to undergo electrolytic dissociation. 

Quantitative Measurements of Conductivity. 

The pure solvents are extremely poor conductors of electricity, their specific 
conductivity being as follows : 

Hydrogen chloride about 0*2 x 10~", 

bromide 0'05xlCr 8 , 

iodide 0'2 x 1(T 6 , 

,, sulphide ,, O'l x 10~ li , 

that of the purest water being - 04 x 10~ 6 . 

The resistances are thus much greater than that of an ordinary sample of distilled 
water. 

The majority of the measurements of conductivity were made in an apparatus 
(fig. 2) consisting of a graduated test-tube with fixed electrodes. 





Fig. 2. 



Fig. 3. 



A sufficient quantity of the solvent was first placed in the conductivity vessel and 
a weighed quantity of the substance under investigation introduced by means of a 

E 2 



124 DR. B. D. STEELE, DE. D. McINTOSH AND DR. E. H. ARCHIBALD 

cooled platinum spoon. The mixture was then stirred until the conductivity remained 
constant, after which the volume of the solution was observed. A further weighed 
quantity of the substance was then introduced and dissolved, and the conductivity 
again measured. The same series of operations was frequently repeated until a 
sufficient number of measurements had been made. 

Other measurements were made in the apparatus shown in fig. 3. This consisted 
of a graduated test-tube A, provided with fixed electrodes, and with a delivery tube 

B attached. 

A saturated solution of the substance was made in the apparatus shown in fig. 1, a 
portion removed for analysis, and a sufficient amount put into the conductivity vessel, 
where its conductivity was measured and the volume noted. More of the solvent 
was then added, and the liquids were well mixed by blowing air through the delivery 
tube B. The volume was again read and the conductivity measured. 

This succession of operations was repeated until the vessel became full of liquid, 
after which a measured volume of the solution was removed, and the operations were 
continued until a sufficient number of measurements had been obtained. 

In all the measurements the electrodes were sufficiently immersed to give the 
maximum conductivity of the apparatus. 

Our results are given in the following tables, which also contain the temperature 
coefficient of conductivity for those solutions which are marked with an asterisk. 

The dilutions, which are given under V, represent the number of litres of solution 
which contain 1 gram-molecule of solute, and the molecular conductivities in reciprocal 
ohmsx 10~ 3 are given under p. The numbers are thus expressed in the same units as 
the molecular conductivity of aqueous solutions as given by KOHLRAUSCH and 
HOLBORN (' Leitvermb'gen der Elektrolyte '). 



TABLE I. Solvent : Hydrochloric Acid. 



V. 


p. 


V. 


/* 


HYDROCYANIC ACID. 


41-4 
21-3 
14-1 
10-2 
9-2 
7-35 


0-51 
0-91 
0-98 
1-08 
1-34 
1-48 


4-90 
4-08 
3-12 
*2-56 
1-79 
1-23 


2-09 
2-83 
3-65 
4-47 
5-81 
7-70 


Temperature coefficient between - 99 and - 95 = - 2 per cent. 
-99" -90 = -1-8 
-99 -85 = -1-3 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 



125 



TABLE 1. Solvent : Hydrochloric Acid (continued). 



V. 



V. 



TRIETHYLAMMONIUM CHLORIDE. 



71-4 
37-0 
20-4 
16-1 
11-6 



9-43 



1-80 
1-80 
2-28 
2-71 
3-15 
3-67 



7-69 


4-37 


6-13 


5-18 


5-00 


6-05 


4-25 


6-73 


3-64 


7-72 


*2-99 


8-51 



Temperature coefficient between - 98 and - 89 = 0-39 per cent. 

-98' -86 = 0-67 



ETHYL OXIDE. 



12-50 


0-14 


5-00 


0-23 


3-12 


0-39 


1-92 


0-95 


1-45 


1-41 



1-09 


. 2-03 


0-88 


2-20 


0-72 


2-90 


0-61 


3-09 



Temperature coefficient between - 99 and - 95 = 1 '9 per cent. 

-99 -90 = 1-8 
M ii ii 99 85 = 1'7 ,, 



ACETAMIDE. 



29-4 


1-59 


12-8 


3-12 


8-62 


4-27 


4-65 


6-39 


4-15 


6-92 



2-86 


8-20 


2-13 


9-41 


1-54 


10-8 


0-95 


12-1 


0-51 


12-3 



Temperature coefficient between - 97 and - 92 = 1 -4 per cent. 

-97 -86= 1-2 
-97 -83= 1-2 



ACETONITRILE. 



21-7 


1-51 


2-17 


6-82 


8-33 


2-44 


1-54 


6-25 


4-76 


3-89 


1-09 


8-OS 


3-22 


5-25 


0-81 


9-61 



126 



DR. B. D. STEELE, DE. D. McINTOSH AND DR. E. H. ARCHIBALD 



TABLE II.- Solvent : Hydrobromic Acidt 



V. 


,. 


V. 


P- 




TRIETHYLAMMO 


VIUM CHLORIDE. 




143 
50 

27-7 
15-6 
8-33 


0-19 
0-22 
0-50 
0-83 
2-00 


5-26 
3-33 
2-17 
1-61 


3-29 
4-90 
6-20 
8-19 


ETHYL OXIDE. 


16-6 
5-55 
4-00 
2-00 
1-54 


0-005 
0-014 
0-024 
0-106 
0-129 


1-23 
1-03 
0-68 
0-47 


0-152 
0-164 
0-182 
0-726 


ACETONE. 


8-33 
5-00 
3-23 
2-00. 


0-10 
0-34 
0-77 
1-40 


1-64 
1 35 
1-07 
0-75 


2-32 
3-24 
4-30 
5-63 


ACETAMIDE. 


90-9 
58-8 
23-3 
14-5 
10-2 


0-06 
0-10 
0-27 
0-42 
0-57 


6-66 
3-85 
3-03 
*2-08 
1-41 


0-94 
1-47 
1-80 
2-37 
3-15 



Temperature coefficient between - 83 and - 77 = 94 per cent. 

-83 -74 = 0-94 

ACETONITRILE. 



33-3 


0-14 


1-47 


4-62 


4-76 


1-08 


1-22 


5-43 


3-70 


1-32 


0-96 


6-99 


2-50 


2-48 


0-72 


10-01 


1-85 


3-46 







ETHYL PROPIONATE. 


12-5 


0-05 


2-63 


0-82 


7-14 


0-16 


1-92 


1-19 


5-26 


0-38 


1-39 


1-69 


3-45 


0-49 






ORTHO-NITROTOLUENE. 


25 


0-04 


3-85 


0-21 


16-6 


0-07 


2-38 


0-45 


12-5 


0-07 


1-50 


0-67 


11-1 


0-10 


0-92 


1-02 


8-33 


0-11 


0-66 


1-28 



t The solutions marked thus t were measured by McINTOSH and STEELE. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 



127 



TABLE II. Solvent : Hydrobromic Acid (continued). 



V. 


p- 


V. 


11. 






1 



200 
21-3 
14-1 



166 
62-5 



62-5 
34-5 



tTETRAMETHYLAMMONIUM CHLORIDE. 



5-40 

8-94 

10-56 



10-5 
9-42 



tTETRAMETHYLAMMONIUM BROMIDE. 



[12-6] 
7-0 



34-5 
11-8 



tTETRAMETHYLAMMONIUM IODIDE. 

8-75 22-2 

10-35 



12-53 
13-30 



7-25 
12-6 



13-10 



TABLE III. Solvent : Hydriodic Acid. 



V. 


/* 


V. 


p. 




TRI ETHYL AMMONIUM CHLORIDE. 


27-8 


0-07 


5-55 


1-15 


21-7 


0-11 


4-50 


1-48 


15-4 


0-23 


3-85 


1-91 


10-4 


0-43 


3-13 


2-37 


8-55 


0-65 


2-50 


2-97 


7-14 


0-80 


2-17 


3-58 


ETHYL OXIDE. 


10-0 


0-02 


1-49 


1-11 


5-88 


0-07 


1-25 


1-40 


3-33 


0-22 


1-06 


1-79 


2-46 


0-61 


*0-88 


2-21 


1-79 


0-84 









Temperature coefficient between - 50 and - 45 = 1 9 per cent. 

-50 -40= 1-8 

ETHYL BENZOATE. 



16-6 


0-014 


2-56 


1-65 


7-14 


0-170 


2-04 


2-30 


4-76 


0-47 


1-66 


2-98 


3-45 


1-02 


1-37 


3-60 



128 DK. B. D. STEELE, DK. D. McINTOSH AND DR. E. H. ARCHIBALD 

TABLE IV. Solvent : Sulphuretted Hydrogen. 



V. 



/* 



V. 



TRIETHYLAMMONITJM CHLORIDE. 



71-4 
12-8 
8-33 



0-12 
0-21 
0-33 



4-00 
3-13 

*2-50 



0-87 
1-17 
1-58 



Temperature coefficient between - 80 and - 75 = 0'88 per cent. 

-80 -70 = 0-90 
-80 , -65 = 0-85 



NICOTINE. 



66-7 
14-3 
6-67 
4-00 



9-09 
1-18 
0-90 



0-03 
0-04 
0-06 
0-16 



0-02 
0-29 
0-39 



2-27 
1-92 
1-03 



0-38 
0-50 
0-76 



PlPERIDINE. 



0-75 

0-64 

*0'55 



0-46 
0-48 
0'50 



Temperature coefficient between - 80 and - 66 = 1 '82 per cent. 

-80 and -63 = 1-84 



TETRAMETHYLAMMONIUM CHLORIDE. 



34-5 
11-0 
4-35 



1-71 
3-41 

3-85 



3-33 
2-93 



4-02 
3-85 



Temperature coefficient between - 70 and - 64 '7 = 0'95 per cent. 

-70 -62-6 J - 1-07 
-70 -60-8= 1-09 



The foregoing results are shown graphically in the figs. 4 to 7, in which the 
molecular conductivities are plotted against the dilutions. It will be seen that in 
every case JJL decreases enormously with dilution, a variation which is exactly opposite 
to that which might be expected from analogy with aqueous solutions. These results 
indicate that, if conduction is due to ionisation, the degree of dissociation decreases 
with dilution, a result which is in opposition to the law of mass action. 

This subject will be discussed fully in Part IV. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 



129 



SOLVENT 
HYDROGEN CHLORIDE 



WOL EQULAF{\ CONBUC T/\VI TY 



5 3-0 3-5 4-0 4-5 5-0 5'5 6-0 65 7-0 7-5 



5 1-0 1-5 2-0 




8-0 es 



VOL. CCV. A 



130 DR. B. D. STEELE, DR. D. McINTOSH AND DR. E. H. ARCHIBALD 



^& 

26 

24 

ft 



OIB 
^ 

' 

14 

tl 

10 
8 
6 
a. 
^ 






































\(% H s 

1 


} 3 /W, 


:i 






































































































































































\ 










SOLVENT 
HYDROGEN BROMIDE. 












\ 


















u \ 


\ 






























I 
































9 


\C/j 


^CQNh 


N 


i 


























(p5 


"V 


\ 






\ 
























\ 




s 






^v>, 


"^ 


^ 






















V 


bx 

~- 


^ 


^nS 


^ C// J 


CN 






"~--o 


*-- 


~- , 


~Q 




















- -j 


**> 


, 


o 


-o 


1 


^ 





c 
>ITY ' 


> 




o 






ULAFt 



5 l-O 1-5 2-0 2-5 3-0 3-5 4-0 4-5 5'0 5-5 6'0 6 

Fig. 5. 



5 7-0 7-5 8-0 8-5 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 



131 



X 

k 



00 



X 
Q_ 



Z <" 

uJ 

> z 



O 
CO 



O 
O 
cc 

O 



I- 



s 

<0 
-<fl 



CO 





Q) <X) 

'/VO/U.H7/C7 



rvj _ 




to 





S 2 



132 DE. B. D. STEELE, DR. D. McINTOSH AND DR. E. H. ARCHIBALD 

As a general rule, the same substances conduct better when dissolved in hydrogen 
chloride than in the other solvents. Next, in the order given, come solutions in 
hydrogen bromide, iodide, and sulphide. An exception to this rule is found in the 
case of ether, which conducts best in hydrogen chloride, and worst in hydrogen 

bromide. 

The conductivity temperature coefficients do not appear to have anything in 
common with the viscosity temperature coefficient, so that the ions cannot be looked 
upon as being surrounded with an atmosphere of the solvent (KOHLRAUSCH, ' Roy. 
Soc. Proc.,' 71, 338, 1903). 

The coefficients are for the most part positive, the conductivity increasing with rise 
of temperature, an exception occurring in the case of hydrocyanic acid dissolved in 
hydrochloric acid. 

The Determination of Molecular Weights. 

The molecular weights were determined by measuring the rise in boiling-point 
which was brought about by the addition of known quantities of the dissolved 
substance. 

Considerable experimental difficulty has been experienced during the progress of 
the work, which has also proved expensive on account of the very large quantities of 
carbon dioxide which were required, and consequently only a few determinations have 
been made. 

The accurate measurement of small differences of temperature at low temperatures 
has been successfully accomplished by the use of a differential method, in which two 
platinum resistance thermometers were employed to measure the temperatures, one of 
the thermometers being immersed in the pure boiling solvent and the other in the 
boiling solution.* 

The thermometers were each made from about 2 metres of 6 mil wire, and had 
exactly the same resistance, which was of such a magnitude that a difference of 1 in 
the temperature of the two coils produced a displacement of 16 '7 millims. in the 
balance point on the bridge. The thermometers were supplied with compensation 
leads in the usual way. The bridge was of the Carey-Foster type. With the 
galvanometer used a difference in temperature of 0'03 C could be detected with 
certainty. 

The apparatus was tested by immersing the two coils in (a) boiling water, 
(b) melting ice, (c) boiling hydrogen sulphide, (d) boiling hydrogen bromide, and 
(e) boiling hydrogen chloride ; the same balance point was obtained in each case. 

The measurements were made in the two pieces of apparatus shown in fig. 8, 

f The bridge and resistance thermometers were lent to us by Dr. H. L. BARNES, through whose advice 
and assistance many difficulties have been avoided. We take this opportunity of expressing our thanks to 
him for his kindness and help. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 



133 




Fig. 8. 

each of which consisted of two concentric tubes, A and B, which were sealed 
together at the top. The outer tube B was provided with the two side tubes C and D, 
to one of which, C, the condenser was attached, the other being closed by a well- 
fitting cork. The two thermometers were placed in A and A', and were held in 
position by waxed corks. 

To carry out an experiment, a sufficient quantity of the liquefied gas was introduced 
through the side tubes D and D' into the vessels B and B', both of which contained 
beads to ensure steady boiling. In order to determine the quantity of solvent used 
in making the solutions, the volume of liquid in one of the vessels was measured at a 
definite temperature, or, if liquid air was available, the liquid was frozen and the 



134 DR. B. D. STEELE, DR. D. McINTOSH AND DR. E. H. ARCHIBALD 

vessel containing it weighed. The condensers were then filled with a mixture oi 
solid carbon dioxide and ether, maintained at atmospheric pressure for the experiments 
with hydrogen bromide and sulphide, and at reduced pressure for the experiments 
with hydrogen chloride. 

After the liquid in the vessels had commenced to boil, the vessels were wrapped in 
natural wool, and the balance point on the bridge was determined. Weighed 
quantities of the substances whose molecular weight was to be determined were then 
successively introduced, and the displacement of the balance point was determined 
after each addition. From these displacements the corresponding rise in boiling-point 
was calculated. The loss by evaporation, due to the high vapour pressure of the 
solvents at the temperature of the condenser, was corrected for by means of a blank 
experiment. 

Evaporation also occurred when the substances were introduced into the apparatus, 
but as this evaporation was proportional to the amount of substance added, a correction 
was easily applied. As a check on these corrections, the boiling-point apparatus was 
removed after each two or three determinations, and when liquid air was available, 
the apparatus was cooled and weighed. When liquid air could not be obtained, the 
tube was cooled to a definite temperature, the volume of solution measured, and the 
amount of solvent calculated on the assumption that no volume change occurred on 
mixing. 

From the data thus obtained the molecular weight constant was calculated by 
means of the formula 



M = 

r< A > 
G A 

in which the molecular weight of the dissolved substance is expressed in terms of y, 
its weight in grammes dissolved in G-gramme of the solvent, and of the corresponding 
rise in boiling-point A, K being a constant in the case of a solute which is neither 
associated nor dissociated. The values of y, G, A, and K for the various substances 
investigated are given in the first four columns of Tables V, VI, and VII. 
The following example will show the method of making the calculations : 

Toluene in Hydrochloric Acid. 

Apparent volume of liquid +0'39# toluene. . 38'3 cub. centims. 

). ,, ,, beads ....... 17'0 

Real volume of liquid ......... 21 - 3 

Volume of toluene ......... . . 0'4 

hydrochloric acid ...... 20 '9 

Weight (Part I.) .......... 25%. 

Rise of boiling-point ......... 0'42. 

Constant ........ = 2480. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 



135 



VAN 'T HOFF has shown that the molecular rise of boiling-point can be calculated 
by means of the formula 

, T _ 0-02T 2 
~W~' 

where T is the absolute temperature and W is the latent heat of evaporation of 
1 gramme of the solvent. 

We have calculated the values for the molecular rise of boiling-point of the various 
solvents by means of the latent heats which are given in Part I. 

The molecular weight of the dissolved substance has been calculated from the values 
so obtained for the molecular rise. 

The molecular weights are given under M' in the sixth column of the tables, and in 
the fifth column the concentrations of the solutions are expressed in grammes of solute 
dissolved in 100 grammes of solvent. 

0-09T 2 
TABLE V. Molecular Weights in Hydrogen Chloride, IT = 720. 



ff- 


G. 


A. 


K. 


C. 


M'. 


TOLUENE. 


0-39 


25-0 


0-42 


2480 


1-56 


26-6 


0-88 


24-5 


0-93 


2380 


3-59 


27-8 


2-25 


24-5 


2-25 


2250 


9-18 


29-4 


3-25 


23-9 


3-35 


2270 


13-60 


29-2 


4-28 


23-9 


4-31 


2210 


17-91 


29-9 


ETHER. 


1-54 


38-4 


0-27 


500 


4-01 


107 


2-99 


36-3 


0-96 


860 


8-24 


61-8 


3-62 


33-9 


1-56 


1080 


10-68 


49-3 


3-62 


30-4 


1-98 


1230 


11-91 


43-3 


4-29 


29-2 


2-95 


1485 


14-69 


35-9 


4-69 


28-4 


3-63 


1630 


16-02 


32-8 


4-69 


25-5 


4-82 


1940 


18-40 


27-5 



136 



DE. B. D. STEELE, DR. D. MoINTOSH AND DR. E. H. ARCHIBALD 



TABLE VI. Hydrogen Bromide, 



-02T 2 



= 1770. 



9- 


G. 


A. 


K. 


C. 


M'. 


TOLUENE. 


1-82 


51-3 


0-77 


2000 


3'54 


81-4 


2-15 


50-3 


1-02 


2200 


4-27 


74-1 


2-71 


49-3 


1-27 


2120 


5-50 


76-7 


;i 45 


48-3 


1-62 


2090 


7-14 


78-1 


ETHER. 


0-39 


38-8 


0-24 


1745 


1-02 


75-1 


0-79 


38-1 


0-48 


1700 


2-09 


77-0 


1-15 


37-4 


0-78 


1870 


3-08 


69-9 


1-69 


36-7 


1-27 


2045 


4-60 


64-1 


2-18 


35-5 


1-95 


2350 


6-14 


- 53-7 


2-64 


34-0 


2-94 


2800 


7-76 


46-7 


3-05 


32 '6 


4-18 


3300 


9-37 


39-7 


ACETONE. 


0'55 


45-4 


0-22 


1060 


1-21 


97-1 


1-23 


42-4 


0-53 


1060 


2-91 


97-1 


1-89 


39-4 


1-20 


1450 


4 '80 


70-7 


2-76 


37-4 


2-94 


2310 


7-38 


4-44 



A-09T 2 

TABLE VII. Sulphuretted Hydrogen, ^=jL = 620. 



9- 


G. 


A. 


K. 


C. 


M'. 












TOLUENE. 


1-25 

2-25 
3-29 
4-22 


22-1 
22-1 
22-1 
22-1 


0-44 
0-72 
1-01 
1-16 


670 
650 
625 
560 


5-64 
11-51 
14-89 
19-10 


79-5 
87-8 
91-4 
102-1 


TRIETHYLAMMONIUM CHLORIDE. 


0-76 
1-30 
1-62 
1-98 


22-6 
22-3 
21-9 
21-6 


0-23 
0-44 
0-60 
0-69 


940 
1040 
1115 
1035 


3-36 
5-83 
7-40 
9-17 


90-7 
82-2 
76-5 
82-4 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 137 



These results may be briefly summarised as follows : 

Toluene, which is a non-conductor in each of the solvents, has an average molecular 
weight of about 30 in hydrogen chloride, 78 in hydrogen bromide, and about 90 in 
sulphuretted hydrogen, and therefore appears to be dissociated when dissolved in 
hydrogen chloride and hydrogen bromide and to a greater extent in the former 
solvent. 

KAHLENBERG ('Jour, of Phys. Chem.,' 1901, v., 344; 1902, vi., 48) has noticed a 
similar anomaly in the case of a solution of diphenylamine in methyl cyanide. 

Ether in hydrogen chloride and hydrogen bromide, and acetone in hydrogen 
bromide have molecular weights which indicate association in the more dilute solvents 
and dissociation in the more concentrated. 

Triethylamine hydrochloride appears to be dissociated when dissolved in sulphur- 
etted hydrogen, the dissociation being greater in the more concentrated solutions. 



VOL. COV. A. 



138 DR. B. D. STEELE, DR. D. MoINTOSH AND DR. E. H. ARCHIBALD 



PART III. 

The Transport Numbers of Certain Dissolved Substances. By B. D. STEELE. 

THE strikingly abnormal variation ot molecular conductivity with dilution that we 
have found to occur in solutions in the liquefied halogen hydrides finds a possible 
explanation in the assumption that it is the solvent and not the solute which is 
ionised. As the transport number of the dissolved substance might be expected to 
yield information not only as to the correctness of this assumption, but also as to the 
constitution of the electrolyte, the transport numbers of a few substances have been 
measured, and the results are given in the following pages. 

The only measurements of the migration ratio which have hitherto been made in 
solvents other than water are those of a few salts in methyl and ethyl alcohol, and ol 
silver nitrate in pyridine and in acetonitrile. 

Direct measurements of the velocities of certain ions in liquefied ammonia have 
recently been made by FRANKLIN and CADY ('Journal of Amer. Chem. Soc.,' 1904, 
vol. 26, p. 499), who used a modification of MASSON'S method (' Phil. Trans.,' A, 1902, 
vol. 192, p. 331). 

Method of Measurement. 

It has been shown by the author (STEELE, 'Phil. Trans.,' 1902, A, vol. 198, p. 105) 
that the direct method of measurement gives trustworthy results only when the salt 
under examination is of the simplest type. Now HITTORF has shown that in 
alcoholic solution cadmium iodide and certain other salts are dissociated into ions 
which are much more complicated than those occurring in aqueous solutions of the 
same concentration. 

The only substances which we have found to be capable of forming conducting 
solutions in any of the solvents which we have been investigating are certain organic 
compounds, and although the nature of the ions into which these dissociate is entirely 
unknown, it is probable that the ionisation is even more complicated than that of 
cadmium iodide dissolved in alcoholic solution. 

From these considerations it was decided to use HITTORF'S method, notwithstanding 
the fact that it is much more tedious and presents greater experimental difficulties 
than the alternative method of direct measurement. 

HITTORF'S method consists in the analysis, after electrolysis, of the solution which 
surrounds one of the electrodes. The original concentration being known, the actual 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 139 

amount of substance which has been carried to the electrode by the current can then 
be calculated. The current is usually measured by a silver voltameter placed in the 
same circuit as the electrolytic cell. The calculation, neglecting certain small 
corrections, is as follows : 

If x grammes of the substance, whose equivalent weight is n, be transported by 
the current which deposits y grammes of silver on the cathode of the voltameter, 

then the transport number of the cation is given by p = . p represents the 

u 
fraction of the total current which is carried by the cation, on the assumption that 

one unit charge of electricity is associated with one equivalent of the dissolved 
substance. It is probable that this condition is fulfilled only in solutions of salts of 
the simplest type (STEELE, loc. cit.). 

Preparation of Solutions. 

The most convenient refrigerant which was available was a mixture of carbon 
dioxide and acetone, and as at the temperature of this mixture hydrogen chloride 
is a gas and hydrogen iodide a solid, the choice of solvent was limited to 
hydrogen sulphide and hydrogen bromide. Solutions in the former solvent are very 
much more difficult to analyse than those in the latter, and accordingly hydrogen 
bromide only has been used as solvent during the investigation. 

The hydrogen bromide was prepared and purified by the method described in 
Part I. In order to make the solutions for electrolysis, the gas was condensed in a 
graduated vessel in which a sufficient quantity of the substance under examination 
had been placed, the condensation being stopped as soon as the desired volume of 
solution had accumulated. 

A quantity was usually made sufficient for two experiments, and by placing the 
receiver in a good silvered vacuum vessel with a stiff paste of the carbon dioxide and 
ether, the solution could be kept for a period of twenty hours without renewal of the 
refrigerant. The apparatus in which the electrolysis was carried out was immersed in 
a bath of solid carbon dioxide and acetone contained in a large cylindrical silvered 
vacuum vessel. This mixture can be maintained at a practically constant tempera- 
ture by blowing a steady stream of air through it ; the temperature, moreover, may 
be varied within certain limits by altering the rapidity of the air current. 

The Validity of FAEADAY'S Law. 

The measurement of the transport number depends on FARADAY'S law, and although 
this is known to hold rigidly for aqueous solutions, there is no evidence as to its 
validity for solutions such as those under investigation. Experiments were therefore 
undertaken with the object of testing the law. 

This was accomplished by comparing the weight of silver deposited in a voltameter 

T '2 



140 DR. B. D. STEELE, DE. D. McINTOSH AND DE. E. H. ARCHIBALD 

with the volume of the hydrogen evolved at the cathode during the electrolysis of 
solutions in hydrogen bromide. The apparatus used (fig. 1) consisted of a tube A 
with a coiled platinum wire p sealed through the bottom and projecting about an inch 

into the tube, the stem of the projecting part being 
covered with blue enamel glass. Electrical contact with 
this electrode, which was used as cathode, was made by 
means of mercury contained in the tube b. The inner 
cell C was provided with a long capillary d, which 
passed through the rubber cork e, and served for 
delivering the hydrogen into a measuring tube. The 
anode g consisted of a ring of platinum wire, which was 
attached to the tube /. 

In carrying out the experiments the tube A was first 
immersed in a bath of carbon dioxide and ether ; the 
solution to be electrolysed was then run in, and C, which 
had been previously cooled, placed in position. A silver 
voltameter was then placed in the circuit, and current 
from a battery of about 60 volts was passed through the 
cell. The hydrogen evolved in A escaped through d, 
and was collected and measured. 

Two experiments of this nature were carried out, the 
details of which are as follows : 

Experiment 1. Solution of diethylamine in hydrogen 
bromide. E.M.F. = 50 volts. Current = 0'091 ampere. 
Silver deposited in voltameter = 0'1894 gramme, 

equivalent to 19 '8 cub. centims. hydrogen at and 760 millims. Hydrogen 
evolved = 19'7 cub. centims. at and 760 millims. 

Experiment 2. Solution of acetophenone in hydrogen bromide. E.M.F. = 60 volts. 
Current = 0'190 ampere. Silver deposited in voltameter = 0'1661 gramme. Hydrogen 
equivalent = 17 '31 cub. centims. at and 760 millims. Hydrogen evolved = 17 '3 8 
cub. centims. at and 760 millims. 

These experiments were considered sufficient to show that FARADAY'S law is valid 
for solutions of organic substances in hydrogen bromide. 




Fig. 1. 



The Method of Analysis. 

As the total increase in concentration which had to be measured amounted to only 
a few centigrammes, it was necessary to carry out the analysis with a high degree of 
accuracy. This was found to be extremely difficult on account of the very high 
vapour-pressure of hydrogen bromide even at temperatures near its freezing-point, 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 



141 



and it was only after months of failure that an apparatus was designed, by means of 
which sufficiently accurate analyses were obtained. 

The apparatus consisted of two parts, the transferrer and the absorber. 

The transferrer (T, fig. 5, see p. 144) consisted of a wide H-shaped tube, with a 
capillary tube a passing through three of its branches, the two tubes being sealed 
together at b and &', as shown in the figure. By filling the space between the tubes 
with a mixture of carbon dioxide and ether, the capillary between 6 and I' could be 
cooled to 81. In fig. 5 the transferrer is shown when placed in the electrolytic cell. 

The absorber (fig. 2) consisted of a stoppered tube A, connected by C with the 




-e 



Fig. 2. 



Fig. 3. 



bubbler B ; this bubbler was so constructed that it was impossible for water to be 
either ejected from the apparatus or sucked back into A. A smaller vessel b of the 
same type was contained within the apparatus. The calcium chloride tube d, which 
was provided with a stop-cock, was attached to B by a ground joint. 

The method of using the apparatus was as follows : A quantity of moist garnets 
were first placed in the tube A, and a quantity of glass beads in the section c of the 
absorber. The requisite amount of distilled water was then placed in the bubblers B 
and b, and the tube d and stop-cock f were replaced. The apparatus was then 
weighed, a glass counterpoise of approximately the same size, shape, and weight being 
used. The tube A was next immersed in a mixture of solid carbon dioxide and ether, 
and after the cap k, fig. 3, had been placed in position by means of the rubber cork m, 



142 



DR. B. D. STEELE, DR. D. McINTOSH AND DR. E. H. ARCHIBALD 



the limb of a transferrer was passed through k, and the whole apparatus made air- 
tight by means of a piece of rubber tubing, e. 

The object of the cap k was to prevent the limb of the transferrer from coming into 
contact with the rubber grease, with which the stoppers were lubricated, and it was 
constructed so that when in position its narrow portion was exactly in the axis of 
the tube g. 

The transferrer was then packed with the carbon dioxide and ether mixture, and 
the hydrogen bromide blown into A by means of a small indiarubber bellows. The 
rubber tube e was then cut away, after which the transferrer and then the cap k 
were removed, and the stop-cock f was re-inserted. 

The tube A was finally removed from the cold bath and the hydrogen bromide 
allowed to boil off. This always took place steadily, provided the vessel contained 
moist beads or garnets ; in the absence of these, or if they were dry, the violent 
bumping which resulted was liable to blow out one or other of the stoppers. The 
hydrogen bromide as it boiled off passed through C, and was almost completely 
absorbed at the surface of the water in the outer portion of B ; a small quantity ot 
gas bubbled through the hole h and was absorbed inside ; very occasionally a few 
bubbles passed through b, where any traces of acid which might have passed through 
the larger portion of the apparatus were absorbed. After all the hydrogen bromide 

had evaporated the stop-cock e was closed, the 
apparatus immersed in distilled water, carefully 
wiped and again weighed, the necessary correction 
being made for the increase of volume of the liquid 
contained in it. The increase in weight gave the 
amount of solution that had been used. The 
contents of the absorber were next washed into a 
large beaker and the hydrogen bromide determined 
by titration with a twice normal alkali solution, 
which had been carefully standardised and was free 
from carbonate. The difference between the amount 
of acid found in this manner and the amount of 
solution actually weighed gave the weight of the 
dissolved substance. The alkali was contained in 
a weighing burette of the pattern shown in fig. 4. 
In order to deliver from this burette, the cap 6 was 
removed and the stop-cock opened, when by blowing through the side tube d the 
liquid was forced through the tube c. The burette was weighed to 0-002 gramme, a 
glass counterpoise of approximately the same volume being used. 

Phenolphthalein was used as indicator, and an excess of one or two drops of alkali 
added, the exact amount of excess being determined by titration with a twentieth 
normal solution of hydrobromic acid. 



d. 




Fig. 4. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 143 

In order that the determination of acid by titration should be strictly comparable 
with the weighing of the solution, the alkali was standardised by direct comparison 
with about 60 grammes of pure hydrogen bromide which was weighed in the absorber. 
Duplicate standardisations of the same alkali solution gave the following figures for 
the amount of hydrobromic acid equivalent to 1 gramme of alkali solution : 

(1) 1 gramme solution = 0'149293 HBr, 

(2) 1 0-149301 HBr. 



The Electrolysis. 

In designing an electrolytic cell it was necessary to consider the changes of density 
which were brought about during electrolysis, and to construct an apparatus in which 
the lighter solution would be formed at the top and the heavier at the bottom. 
Preliminary experiments were undertaken to ascertain the influence of an increase in 
concentration of the dissolved substance on the density of the solution, and it was 
found that in all the cases examined the less concentrated solution was the heavier. 

The experiments which had been conducted to test FARADAY'S law having shown 
that the bromine is carried to the anode, the apparatus was designed to enable the 
cathode solution to be analysed. The anode solution was neglected, as its analysis 
was complicated by the presence of bromine. 

The apparatus which has been employed is shown diagrammatically in fig. 5. It 
consisted of a U-tube, both arms of which were provided with side tubes. The 
anode a consisted of a platinum wire, which was sealed through the bottom of the 
side tube 0, the other end of the wire projecting into the glass tube h, by means of 
which connection with the battery could be made. A small side tube n was also 
attached to the same arm of the U-tube, and there was a constriction at r into which 
the hollow stopper s was ground to fit tightly. The stopper A- was sealed to a branch 
of the transferrer T', and a hole was bored in its shoulder to allow the free passage of 
liquid through the transferrer. 

It was found in the preliminary experiments that a considerable amount of mixing 
was occasioned by the escape of hydrogen at the cathode, and in order to reduce 
this to a minimum, the side tube P was attached to the apparatus. In the centre 
of P a narrow tube u was fastened, inside which the cathode was placed, so that the 
escaping bubbles of hydrogen were confined to this tube and very little mixing took 
place outside P. A small hole had been blown in the wall of the tube u so that the 
pressure should be equal at all parts of the surface of the liquid. The tube P was 
made long enough to be held in the clamp outside the vacuum vessel in which the 
apparatus was placed and its end was closed by a stopper w, through which passed 
the platinum wire which was used as cathode. One end of the transferrer T was 
made long enough and bent so as to reach to the bottom of the U-tube, and both the 



144 DR. B. D. STEELE, DR. D. McINTOSH AND DR. E. H. ARCHIBALD 

transferrers were attached to the open ends of the main apparatus by pieces oi india- 
rubber tubing, t and t'. 




Fig. 5. 

In carrying out an experiment the method of procedure was as follows : The 
apparatus was placed in the vacuum vessel and held rigidly by a clamp which 
grasped the tube P. The open ends of the transferrers T and T' were then closed by 
rubber tubing and glass plugs, and a tube filled with phosphoric oxide was attached 
to n. The stop-cock w with the cathode attached was then removed and a third 
transferrer (not shown in the figure) inserted in the tube P. The acetone was then 
placed in the vacuum vessel and solid carbon dioxide added till the temperature had 
fallen to the desired point. The outside arm of the third transferrer was provided 
with a filter of glass wool and reached to the bottom of a vessel containing 10 cub. 
centims. more of the solution than was necessary for the electrolysis. After the 
whole of this liquid had been forced into the apparatus by blowing air from a rubber 
bellows into the vessel containing the liquid, the transferrer was removed and the 
stopper w replaced. 

Before commencing the experiment three absorbers had been filled with distilled 
water and weighed. The transferrer T was next attached to one of these in the 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 145 

manner previously described and 10 cub. centims. of the solution were taken out and 
analysed. This analysis gave the concentration of the solution before electrolysis. 
A silver voltameter and a milliampermeter having been placed in the circuit, the 
electrolysis was started by connecting the electrodes to the terminals of a battery, 
the voltage of which could be varied within wide limits, and the voltage was adjusted 
so as to give a current of not more than 12 or 14 milliamperes. If a larger current 
than this was employed, the heating effect was found to cause mixing of the liquid 
by convection. After the electrolysis had been continued for about two hours it was 
stopped by removing the cathode from the voltameter, and the liquid in the cell was 
separated into two portions by inserting the stop-cock ,s into its socket. An absorber 
was then attached to the transferrer T' and the column of liquid contained within 
the dotted lines was blown into the absorber, which was then removed. The third 
absorber was next attached to the transferrer T and the solution contained in the 
apparatus forced into it by blowing through w, the tube r acting as a syphon to 
remove the liquid contained in P, and finally the third absorber was removed and 
weighed. Three solutions were thus obtained for analysis, namely: (1) the 10 cub. 
centims. which had been removed before electrolysis and gave the original concen- 
tration ; (2) the small quantity taken out in the second absorber (which should be of 
the same concentration as (1)); and (3) the solution surrounding the cathode, which 
gave the change of concentration brought about by the electrolysis. 

In order that an experiment should be successful it was necessary that the foregoing 
procedure should be strictly followed. Identical values for the original concentration 
and that of the middle portion have never been obtained unless the whole solution 
was first placed in the apparatus and all three portions were taken from it. 

At least half-a-dozen other methods have been tried without success. Fortunately 
it is easy at the close of an experiment to see if any mixing has taken place, from the 
fact that bromine is liberated at the anode, where it forms a deep red solution in 
the hydrogen bromide. If the experiment has been successful, this solution remains 
as a very clearly defined layer surrounding the anode, and the coloration does not 
extend more than about 1'5 centims. up the tube. On the other hand, if mixing has 
taken place, as may happen either if the current is too large or if the temperature of 
the bath is allowed to vary, the bromine is distributed throughout the solution and 
no clearly defined layer is seen at the anode. 

Experimental Results. 

The results of the experiments are contained in the following table, in which the 
concentration of the various solutions is expressed under N, which gives the number 
of gramme equivalents of dissolved substance per litre of solution, the percentage also 
being given in the 3rd column. The 4th column contains the weight of silver 
deposited on the cathode of the silver voltameter, the 5th column gives the weight of 
substance transported, the 6th column the cation transport numbers. 

VOL. cov. A. u 



146 



DR. B. D. STEELE, DR. D. McINTOSH AND DR. E. H. ARCHIBALD 



Number 
of experiment. 


N. 


Percentage 
of composition. 


Deposited in 
cathode. 


Transported. 


f 


1 
SERIES 1. ETHER. N = 1 approximately. 


2 
3 

7 


1-07 
1-14 
1-06 


3-96 
4-26 
3-92 


0995 
0918 
1120 


0567 
0530 
0607 

Mean = 


83 
82 
79 


82 


SERIES 2. ETHER. N = 1-7 to 2-04. 


6 
8 
17 


1-72 
1-80 
2-04 


6-61 
6-85 
8-03 


0988 
0997 
0918 


0489 
0212 
0366 


73 
31 
58 


SERIES 3. TRIETHYI.AMMONIUM BROMIDE. N=-5to-75. 


5 
9 
10 


75 
515 
622 


6-54 
4-47 
5-37 


1064 
0921 

0817 


0-382 
0-288 
0-300 

Mean = 


21 
18 
22 


20 


SERIES 4. 


TRIETHYLAMMONIUM BROMIDE. N = 1-04. 


11 

12 


1-04 
1-05 


8-98 
9-01 


0907 
1051 


0473 
0700 

Mean = 


31 
39 


35 




SERIES 5. ACETONE. N = TO. 


15 
16 


1-05 
1-01 


2-98 
2-87 


0863 
0938 


0151 
0141 

Mean = 


41 
36 


38 




SERIES 6. ACETONE. N = 1-8. 


13 
14 


1-83 
1-82 


5-37 
5-32 


0931 

0878 


0361 
0372 

Mean = 


91 
99 


95 


SERIES 7. METHYLHEXYLKETONE. 


18 
19 


90 
90 


5-34 
5-36 


0965 
0880 


0398 
0384 

Mean = 


38 
41 


39 


SERIES 8. METHYLHEXYLKETONE. 


20 
21 


1-80 
1-80 


11-83 
11-87 


1015 
0943 


0815 
0830 

Mean = 


75 
82 


77 



ON THE HALOGEN HYDEIDES AS CONDUCTING SOLVENTS. 



147 



SUMMARY. 



Substance. 


N. 


Mean value of p. 


Ether 


1 -0 


82 


Triethylammonium bromide .... 
.... 

!> .... 

Acetone 


0-5 
0-62-0-75 
1-04 
1-0 


18 
2-2 
35 
38 




1 -82 


95 


Methylhexylketone 


0-9 


39 




1-8 


77 


: 







With the exception of Nos. I and 4, which unfortunately were lost, all the 
experiments which have been made are given in the tables. The transport number 
of each substance has been measured at two concentrations, the more conceTitrated 
solution usually containing about twice as much solute as the other. It will be seen 
that the cation transport number is always increased by increase of concentration and 
that the amount of disagreement between parallel experiments, although in some 
cases approaching 10 per cent., is never sufficient to leave any doubt as to the influence 
of change of concentration. This change from analogy with aqueous solutions 
indicates an increase in the complexity of the cation as the solution becomes stronger, 
but the measurements of conductivity and of the molecular weight, which are given in 
Part II., do not appear to confirm this conclusion. The significance of the change 
will be discussed in Part IV. 

A special significance is to be attached to the results of Series 2, for the following 
reasons : In the foregoing description of the method of analysis it has been explained 
that after the solution was transferred to the absorber the hydrogen bromide was 
allowed to evaporate and to become dissolved in the water. During the evaporation 
the temperature of the liquid in A gradually rose until finally it reached that of the 
atmosphere, when the liquid which remained was a saturated solution of hydrogen 
bromide in ether. 

At this stage little or no decomposition occurred in a solution which had not been 
electrolysed, or in a dilute solution which had, but in the case of the cathode portion 
of a concentrated electrolysed solution the decomposition which occurred was sufficient 
to give results so discordant as those tabulated in Series 2. This behaviour seems to 
indicate the formation at the cathode of some extremely unstable substance during 
the electrolysis of these solutions, and it is possible that a compound is formed by the 
union of two or more discharged cations by a reaction similar to that by which 
persulphuric acid results from the electrolysis of sulphuric acid. 



u 2 



148 DR. B. D. STEELE, DR. D. McINTOSH AND DR. E. H. ARCHIBALD 



PART IV. 

The Abnormal Variation of Molecular Conductivity, etc. 

i 

By B. D. STEELE, D. MC!NTOSH and E. H. ARCHIBALD. 

IN discussing the nature of those inorganic liquids which are able to act as " ionising" 
solvents, WALDEN (' Zeit. fur anorg. Chemie,' 1900, 25, p. 209) states that "a 
measurable dissociation (ionisation) occurs only in combinations of the elements of the 
5th and 6th groups of the periodic table and in compounds of these elements with 
hydrogen and the halogens." We have shown in Part I. of this investigation that 
the hydrides of the halogen elements and of sulphur belong to the class of " ionising " 
solvents, so that this class consists of compounds of the elements of the 5th, 6th, and 
7th groups amongst themselves and with hydrogen. Attempts have been frequently 
made to arrive at some generalisation connecting the so-called " ionising" power with . 
certain physical constants of the pure solvents. 

Thus, according to NERNST and THOMSON, a close relationship exists between the 
dissociating power and the dielectric constant. These investigators were led to look 
for this relation by the consideration that the force with which two electrically 
charged bodies attract or repel each other depends on the magnitude of the dielectric 
constant of the separating medium, and as the ions are to be regarded as electrically 
charged bodies, the force attracting two unlike ions will be more weakened, and 
dissociation aided, in a solvent of high than in one of low dielectric constant. 

This expectation is only partially realised in the parallelism which exists for a great 
number of solvents between the two properties in question ; thus liquefied ammonia 
which possesses a low dielectric constant is a better dissociating solvent for some 
substances than water which has a high dielectric constant ; moreover, the majority 
of electrolytes are far more dissociated in water than in hydrocyanic acid or in 
hydrogen peroxide, although the dielectric constant of water is less than that of 
either of these liquids. No measurements of the dielectric constant of the halogen 
hydrides or of sulphuretted hydrogen have yet been made. 

DUTOIT and ASTON (' C. R.,' 1897, 125, p. 240) have attempted to show that ionic 
dissociation occurs only in solvents in which the molecules are associated, but, 
although numerous instances occur in which this parallelism obtains, it is by no 
means a general rule. Thus, although both ammonia and sulphur dioxide are 
unassociated liquids, both are able to form conducting solutions ; and although the 
hydrides of bromine, iodine, and sulphur are unassociated, and hydrogen chloride is 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 149 

associated, all four compounds are equally able to act as conducting solvents, whilst 
this property is not possessed by hydrogen phosphide, which is associated. 

BRUHL (' Zeit. Phys. Chem.,' 1898, 27, p. 319) has pointed out that unsaturated 
compounds, as a rule, are good conducting solvents. A consideration of the non- 
conducting unsaturated solvents phosphorus hydride and trichloride, and of the 
conducting saturated solvent phosphorus oxychloride, is sufficient to show that this is 
not a general rule. 

The heat of vaporisation (OBACH, 'Phil. Mag.,' 1891, (5), 32, p. 113) is a fourth 
property which has been suggested as being intimately connected with the dissociating 
power of the solvent. In this case, as in that of the others considered, the connection 
is very obscure and many exceptions occur. 

The temperature coefficients of conductivity and of viscosity are approximately 
equal in the case of aqueous solutions. This is not so in solutions in the solvents 
examined by us, although in these, also, a rise of temperature conditions an increase 
of conductivity and a decrease of viscosity. It is interesting to note that the 
increase of conductivity is, in nearly all cases, greater than the decrease of 
viscosity. 

The foregoing summary shows that failure has attended every attempt which has 
been made to express the power of forming conducting solutions as a function of the 
solvent only. 

As a matter of fact, every solvent exhibits a very marked selective action an 
regards the nature of the conducting solute. Thus water dissolves the majority of 
salts to form solutions which conduct the current ; organic bodies also, other than 
salts, are in many cases soluble, but the solutions are not conductors. Hydrocyanic 
acid behaves similarly to water, but only a few salts are appreciably soluble in this 
solvent. Ammonia, sulphur dioxide, and some other solvents form conducting solu- 
tions, not only with many salts, but also with a few organic substances not usually 
classed as electrolytes. The halogen hydrides, on the other hand, form conducting 
solutions with non-saline organic substances, as well as with salts of the ammonium 
bases, but such solutions are not formed with metallic salts. 

It is evident, therefore, that the ability to form a conducting solution is a function 
of both the solute and the solvent, and this has been recognised in the various 
attempts that have been made to connect the ionising power of a solvent with its 
tendency to form compounds with the solute. Indeed CADY ('Jour. Phys. Chem.,' 
1897, 1, p. 707) was led to investigate the conductivity of solutions of substances in 
ammonia from the analogy between the water and the ammonia compounds of copper 
sulphate. 

KAHLENBERG and SCHLUNDT (' Jour. Phys. Chem.,' 1902, 6, p. 447) express the 
opinion that conductivity is due to mutual action between the solute and the solvent ; 
and an attempt to obtain experimental evidence in support of this view has been 
made by PATTEN (' Jour. Phys. Chem.,' 1902, 6, p. 554). 



150 DR. B. D. STEELE, DR. D. McINTOSH AND DR. E. H. ARCHIBALD 

For many solvents the substances which dissolve to form conducting solutions may 
be broadly designated as those which enter into combination with the solvent. 

Thus the metallic salts as a class are characterised by their tendency to form 
compounds with water, while non-saline organic bodies as a class are not able to form 
such compounds.* Many, but not all, salts which form ammonia compounds dissolve 
in ammonia to form conducting solutions. 

Compounds of the solute with the solvent are also clearly indicated in the case of 
many conducting solutions in sulphur dioxide, and WALDEN and CENTNERSZWER 
(' Zeit. Phys. Chem.,' 1903, 42, p. 432) have isolated and investigated two such 
compounds containing potassium iodide and sulphur dioxide. 

In the halogen hydrides we find that the only substances which conduct are the 
amines, alcohols, ethers, ketones, &c., all of which are able to enter into combination 
with the solvents. Many similar cases have been observed amongst organic solvents, 
and as an example of these reference may be made to solutions in amylamine 
(KAHLENBERG and RUHOFF, ' Journ. Phys. Ch.,' 1903, 7, p. 254). 

The study of the behaviour of aqueous solutions has led to ARRHENIUS' theory 
of ionic dissociation and to VAN 'T HOFF'S theory of solutions ; and numerous 
investigations have been undertaken with the object of testing these theories, when 
applied to solutions in non-aqueous solvents. 

As a result it has been found that, as required by the theory, most substances, 
when dissolved in ammonia, sulphur dioxide, hydrocyanic acid, and some other 
solvents, show an increase of the molecular conductivity, /j., with dilution, but that 
the opposite change occurs in solutions of a few substances in the same solvents. 
This difference in behaviour cannot therefore be conditioned by the nature of the 
solvent only, although if we consider the inorganic hydrides as solvents, we find 
that n varies normally, that is to say, increases with dilution, in solutions in water 
and ammonia, hydrides, namely, of elements in the first series of the periodic table, 
whereas /A decreases with dilution in solutions in the remaining hydrides, the variation 
therefore being abnormal, t 

The results of the molecular weight determinations in non-aqueous solvents are, as 
a general rule, not concordant with the conductivity results, many conducting 
solutions being known in which, contrary to expectations, the dissolved substance 
appears to be associated. 

* The view that compounds of the solute and the solvent exist also in solutions appears to be steadily 
gaining ground, see MORGAN and KANOLT ('Jour. Amer. Chem. Soc.,' 1904, 26, p. 635) and JONES and 
GETMAN (' Zeit. Phys. Chem.,' 1904, 49, p. 390). 

t Amongst others the following cases have been observed of solutions in which the molecular 
conductivity decreases with dilution : Silver nitrate, cadmium iodide, and ferric chloride in amylamine 
(KAHLENBERG and RUHOFF, 'Jour. Phys. Chem.,' 1903, 1, p. 284); Antimony bromide and phosphorus 
pentabromine in bromine (PLOTNIKOFF, 'Jour. Russ. Phys. Chem. Soc.,' 1902, 34, p. 466 ; 1903, 35, p. 794) ; 
Hydrogen chloride in ether and in amyl alcohol (KABLUKOFF, 'Zeit. Phys. Chem.,' 1889, 4, p. 429); 
Hydrogen chloride in cineol (SACKUR, 'Ber. D. Chem. Ges.,' 1902, 35, p. 1242), &c. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 151 

The consideration of these abnormalities has led KAHLENBERG to conclude that the 
theory of ionic dissociation is not applicable to the majority of conducting solutions. 

It is our object to show that the abnormal behaviour of solutions in the solvents 
examined by us can be simply and consistently explained in terms of the theory of 
ARRHENIUS, if the assumption is made that the original dissolved substance, being 
itself incapable of undergoing ionic dissociation, either polymerises or combines with 
the solvent to form a compound containing more than one molecule of the solute, and 
that the polymer, or compound, as the case may be, then acts as the electrolyte. 

Those non-saline organic substances which are able to conduct the current when 
dissolved in certain solvents are considered by WALDEN (' Zeit. Phys. Chem.,' 1903, 
43, p. 385) to be abnormal, in view of their usually well-known constitutions and their 
behaviour in aqueous solutions, but if the foregoing assumption of the formation of 
compounds be made, these substances are not more abnormal electrolytes than 
ammonia, which with water forms the compound ammonium hydroxide. 

It has been suggested that the existence of compounds of the solute with the 
solvent is proved by the abnormal variation of the molecular conductivity, to which 
reference has been made ; but the following considerations will show that an increase 
of fi with dilution furnishes no evidence for or against the occurrence of such 
compounds. 

Let us suppose that a reaction between the solute, AB, and the solvent, CD, takes 
place according to the equation 

AB + CD^AB, CD, 
and let 

a b c 

be the active masses of the three substances. 

Now, provided that moderate dilutions are used, we are justified in regarding b as 

constant, when from the law of mass action - = constant. 

a 

Now if conduction is due to the dissociation of the compound ABCD, the number 
of dissociated molecules is given by etc, where a is the degree of ionic dissociation ; 
but c = Ka ; therefore the concentration of the ions is equal to poiKa if p is the 
number of ions formed from one molecule of solute. 

But the specific conductivity K of the solution is proportional to the ionic 

concentration, and therefore 

K = paJcKa = a.K'a (l), 

and since the molecular conductivity 



K 



= - = aK', 
a 



it must vary with a, that is to say, it must increase with dilution even when a 
compound of the solute with the solvent is formed. 



152 DR. B. D. STEELE, DR. D. McINTOSH AND DR. F, H. ARCHIBALD 

This is the case, for example, in an aqueous solution of ammonia, to which reference 
will be made later. 

If, however, we assume that two or more molecules of AB unite to form a compound 
which undergoes ionic dissociation, AB itself being unable to conduct the current, 
then the molecular conductivity may decrease with dilution whether the solvent 
enters into the composition of the electrolytic compound or not. 

If we consider the two cases : 

(1) A compound of n molecules of solute with m molecules of solvent is formed 
according to the equation 

n (AB) +m (CD) ^ (AB). (CU) mf 
the active masses being 

a b and c. 

Then, if we again consider sufficiently dilute solutions, b may be regarded as 

constant, and 

ka n = k'c or c = Ka". 

If ionic dissociation occurs so that a* of the compound is ionised, then, as before, 
the ionic concentration = pa.c = paKa*. 
The specific conductivity 

K = pVaKa" = aK'a" (2). 

The molecular conductivity 

a = - = aKV- 1 . 

a 

and since the dilution 

V = - 

a' 

K = aK'V-", 
or 

cV- = aK'. 

* In the development of this relation no .assumption has been made us to the nature of the ionisation 
of the electrolyte. 

If we consider the second case, for example, there are a number of ways in which the compound A,,B,, 
can ionise. 

Thus Q 

(1) A n B, t 7-*- ABn-i + B. 



(2) AA-^Att + 
and generally 

(3) A n B n -^-AA 

If dissociation takes place according to the first of these equations, 2 ions result from the dissociation 
of 1 molecule of the electrolyte. 

If according to the second equation, the number of ions is (n+1), and, generally, the number is (r+l). 

Now whatever value r may have, the number of ions present is given by a (r+l) and is therefore 
proportional to a. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 153 

(2) Combination between the solute and the solvent does not occur, but an ionising 
polymer of the solute is formed. In this case the equation is 



A B B,,, 
the active masses are 

a and c, 
and from the law of mass action 

lea* = k'c and c - Ka", 
which leads to the same expression as before, namely 

K = KV, p = aKV-', and *V" = K'. 

Now, since the number of molecules always increases with dissociation, must 
increase with dilution in whatever manner dissociation takes place ; but unless the 
increase in a is greater than the diminution in a"" 1 which is brought about by 
dilution, the sum of the effects due to the variation of a and of a"' 1 in the equation 



/,-! 



p = aK'a* 

must produce a diminution in p. with increasing dilution. 

It follows, therefore, that the molecular conductivity may decrease with dilution 
in the case of any conducting solution in which the electrolyte is a compound of two 
or more molecules of the dissolved substance, whether it is a simple polymer or a 
compound containing one or more molecules of the solvent. 

It follows, also, from the equation 

K = aK'a n 

that in the case of a solution in which the ionic dissociation was approaching 
completion, in which a therefore varied but slightly, the specific conductivity of the 
solution should be very nearly proportional to the n th power of the concentration of 
the dissolved substance ; for such solutions we therefore have the relation 

JL = ,cV" = K'. 

Although we have shown that it is not necessary that union with the solvent 
should occur in order to bring about an abnormal variation of p, we nevertheless 
consider that the formation of such compounds* affords the best explanation of the 
behaviour of solutions of organic substances in the halogen hydrides and in 
sulphuretted hydrogen. 

* See also WALKER, 'J. C. S.,' 1904, vol. 85, p. 1082, and WALKER, MC!NTOSH, and ARCHIBALD, 
'J. C. S.,' 1904, vol. 85, p. 1098. 

VOL, CCV, A, X 



154 DE. B. D. STEELE, DE. D. McINTOSH AND DE, E. H. AECHIBALD 

We are led to this conclusion by a consideration of the following facts : 

(1) Large quantities of heat are evolved when conducting solutes are added to 
either of these solvents. This heat evolution we take to indicate chemical union. 

(2) Compounds containing a varying number of molecules of solvent have been 
isolated (ARCHIBALD and MC!NTOSH, 'Jour. Chem. Soc.,' 1904, vol. 85, p. 919). 

(3) The ionisation of a compound such as ((CH 3 ) 2 CO), l HBr is much easier to 
understand than that of a simple polymer such as ((CH 3 ) 2 CO) n . 

In order to apply the foregoing conclusions to a specific case, we will consider a 
solution of acetone in hydrogen bromide. 

According to our hypothesis, such a solution contains a compound of acetone and 
hydrogen bromide, the formula of which we will assume to be Ac 3 (HBr) Bl . 

This compound dissociates simultaneously in two different ways, a certain number 
of molecules being dissociated into acetone and hydrogen bromide, other molecules 
being dissociated into ions, and the ratio of the number of molecules undergoing each 
dissociation will be constant. 

Applying the equation ^ = K'a s , we see that the molecular conductivity will 
increase with increasing concentration of the acetone, the increase neglecting 
variation of a being proportional to the square of the concentration. Similarly, we 
see that if a is nearly constant, the specific conductivity will be proportional to the 
cube of the acetone concentration. If, however, a is not constant, then K/a will be 
proportional to the cube of the acetone concentration. 

This conception of an intermediate compound which is able to break up in different 
ways is by no means new to chemists, and the solution of ammonia, which we have 
already referred to, furnishes an example of such a case, which, in many ways, is 
analogous to the preceding. 

The compound that is formed in this solution is ammonium hydroxide, and the 
dissociations are 

(1) NH 4 OH:zNH 3 +H 2 0; 

(2) NH 4 OH - NH 4 + OH. 

The relation between specific conductity and concentration for such a solution 
has been already developed in equation (1) K = aK'a, which is a special case of 
equation (2). Here again 

K T7" / 

M---.K', 

so that 

a = ; but a = JL 
K ^ 

so that K' is simply the molecular conductivity at infinite dilution. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 155 

In order to test the conclusions that have been arrived at, we require to know the 
concentration of the unassociated solute for each dilution. 

If A gram-molecules of the solute are dissolved in one litre of solvent, and if 
there are formed c gram-molecules of the electrolytic compound, then, if n molecules 
are required to form one molecule of the compound, nc molecules of solute will have 
been used, when equilibrium is established, so that the equilibrium equation is 

k(A-nc) a = k'c, 
or 

c = K (A-wc)", 

and the general expression for the specific conductivity becomes 

ic = aK'(A-wc)". 

No solution of any substance in any one of the halogen hydrides lias yet been 
found with high value for the conductivity, a fact which may be assigned to one of 
three causes, namely, either (1) the concentration, or (2) the coefficient of ionisation of 
the electrolyte is small, or (3) the ionic velocities may be very small. If we assume 
the first to be the most probable cause, A nc will not differ much from A, and we 
may without sensible error make use of the values for the total concentration in 
applying the above equation to our results. 

This has been done, the equation being used in the form of /cV" = aK', and the 
results of the calculations are given in Tables I. and II. 

Table I. contains the values of V and of /cV" (or aK 7 ) for those solutions in which 
n = 2, that is, in which two molecules of solute combine with the solvent to form 
one molecule of the electrolyte. Table II. contains the similar value for those 
solutions for which n = 3. 

It will be noticed that in some cases the figures exhibit considerable irregular 
variation. This is to be expected from the fact that the measurements of conductivity 
and of concentration are subject to considerable experimental error. These errors 
were not specially guarded against, as our object was to establish beyond question 
the nature of the variation of p. with V rather than to obtain accurate measurements, 
which, in the present state of our knowledge, would not possess any special value. 

The figures for K at very high dilution are, in some cases, quite valueless as a 
test of our hypothesis, on account of the enormous influence of very slight errors of 
observation at these dilutions. 

The results contained in Tables I. and II. are shown graphically in figs. 1 and 2 
respectively. 



x 2 



156 DE. B. D. STEELE, DE. D. McINTOSH AtfD DE. E. H. AECHIBALD 

TABLE I. 



V 

3.K = V 2 



ACETONITRILE IN HYDROGEN CHLORIDE. 

= 21-7, 8-33, 4-73, 3-22, 2-17, 1-09, 0-81 
= 32-8, 20-3, 18-5, 17-0, 14-8, 8-8, 8-3 



ACETAMIDE IN HYDROGEN CHLORIDE. 

= 29-4, 12-8, 8-62, 4-65, 4-15, 2-86, 2-13, 1-54, 0-95, 0-51 
= 46-7, 40-0, 36-8, 29-6, 28-7, 23'4, 20-0, 16-6, 11'5, 6'42 

TRIETHYLAMMONIUM CHLORIDE IN HYDROGEN CHLORIDE. 

= 71-4, 37-0, 20-4, 16-1, 11-6, 9-43, 7 -69, 6-13, 5-00, 4-25, 3-64, 2-99 
ZK = K-V 2 = 128-6, 667, 465, 437, 3G5, 343, 334, 316, 302, 285, 281, 254 

HYDROCYANIC ACID IN HYDROGEN CHLORIDE. 

V = 41-4, 21-3, 14-1, 10-2, 9-2, 7 -35, 4-90, 4-10, 3-12, 2 -56, 1-79, 1-23 

=>-V 2 = 21-6, 19-6, 14-0, 11-0, 12-0, 10-9, 10-.3, 11-5, 11-5, 11-5, 10'4, 9-4 



ETHER IN HYDROGEN CHLORIDE. 

12-5, 5-0, 3-12, 1-92, 1-45, 1-09, 0'88, 0-72, 0-61 
1-75, 1-15, 1 22, 1-82, 2-05, 2-22, 1-93, 2-08, 1-88 



TETRAMETHYLAMMONIUM CHLORIDE IN HYDROGEN BROMIDE. 

V 200, 21-3, 14-1, 10-5, 9'4 

= K-V 2 = 1080, 190-0, 149-0, 131-0, 125-0 



TETRAMETHYLAMMONIUM BROMIDK IN HYDROGEN BROMIDE. 

= 62-3, 34-5, 11-8 
2 | = 43-7, 25-0, 14-8 

TETRAMETHYLAMMONIUM IODIDE IN HYDROGEN BROMIDE. 

V I = 62-5, 34-5, 22-1 
aK = V 2 = 546, 360, 290 



TRIETHYLAMMONIUM CHLORIDE IN HYDROGEN BROMIDE. 

143-0, 50-0, 27-7, 15-6, 8-33, 5-26, 3-33, 2-17, 16-1 
27-4, 11-0, 13-8, 12-9, 16-6, 17-3, 16-4, 13-5, 13-3 

ETHER IN HYDROGEN BROMIDE. 

16-6, 5-55, 4-00, 2-00, 1-54, 1-23, 1-03, 0-68, 0-47 
083, -078, -096, -212, -199, -187, -170, -124, -341 



ON THE HALOGEN HYDEIDES AS CONDUCTING SOLVENTS. 
TABLE I. (continued). 



157 



V 

O.K = * 



ACETAMIDE IN HYDROGEN BROMIDE. 

90-9, 58-8, 23-3, 14-5, 10'2, 6-66, 3-85, 3'03, 2-08, 1-41 
5-94, 5-88, 6-3, 6-1, 5-8, 6-25, 5-65, 5-45, 4-92, 4-45 



ACETONITRILE IN HYDROGEN BROMIDE. 

33-3, 4-76, 3-70, 2-50, 1-85, 1-47, 1-22, 0-96, 0-72 
4-61, 5-15, 4-80, 6-2, 6-4, 6-8, G'7, G-7, 7-2 



ETHYL PROPIONATE IN HYDROGEN BROMIDE. 

12-15, 7-14, 5-26, 3-45, 2-63, 1-92, 1-39 
62, 1-14, 2-00, 1-7, 2-16, 2-30, 2-28 



ORTIIO-NITROTOI.UENE IN HYDROGEN BROMIDE. 

25, 16-6, 12-5, 11-1, 8-33, 3-85, 2-38, 1-50, 0-92, 0-66 

1-00, 1-1G, 0-87, 1-11, 0-92, 0-71, 1-OG, I'OO, 0-94, 0-845 



PIPERIDINE IN SULPHURETTED HYDROGEN. 

9-09, 1-18, 0-90, 0-75, 0-G4, 0-55 
18, -34, -35, -34, -31, -28 



TETRAETHYLAMMONIUM CHLORIDE IN SULPHURETTED HYDROGEN. 

= 34-5, 11-0, 4-25, 3-32, 2-93 
= 59-4, 37-G, 16-4, 13-4, 11-3 



158 DR. B. D. STEELE, DE. D. McINTOSH AND DE. E. H. AECHIBALD 

TABLE II. 



V. V 3 . 


II 
V. 


KV 3 . 


1 

ACETONE IN HYDROGEN BROMIDE. 


8-33 6-94 
5-00 8-50 
3-23 8-03 
2-00 5-6 


1-64 
1-35 
1-07 
0-75 






6-2 
5-9 
4-9 
3-2 








V. *V 2 . 


aK-V 3 . 


V. 


(cV*. 


aK = V 3 . 


TRIETHYLAMMONIUM CHLORIDE IN HYDROGEN IODIDE. 


27-8 1-95 
21-7 2-4. 
15-4 3-56 
.10-4 4-47 
8-55 5-56 
7-14 5-71 


54 

52 
55 

47 
47-5 
41 


5-55 
4-50 
3-85 
3-13 
2-50 
2-17 


G-38 
6-16 
7-35 
7-42 
7-42 
7-77 


35-4 
30-0 
28-3 
23-4 
18-6 
16-9 


ETHER IN HYDROGEN IODIDE. 






10-0 -2 
5-88 -41 
3-33 -73 
2-46 1-50 
1-79 1-50 


2-0 
2-42 
2-44 
3-69 
2-69 


1-49 
1-25 
1-06 
0-88 


1-65 
1-75 
1-90 
1-94 


2-46 
2-19 
2-01 
1-70 


ETHYL BENZOATE IN HYDROGEN IODIDE. 






16-6 -233 
7-14 1-22 
4-76 2-23 
3-45 3-54 


3-8G 
8-67 
10-6 
12-1 


2 56 
2-04 
1-66 
1-37 


4-22 
4 -69 
4-94 
4-93 


10-8 
9-6 

8-2 
0-68 


TRIETHYLAMMONIUM CHLORIDE IN SULPHURETTED HYDROGEN. 


71-4 8-G 
12-8 2-69 
8-33 2-75 


61-3 

34-4 
22-9 


4-00 
3-13 
2-50 


3-48 
3-66 
3-95 


13-9 
11-5 

y-88 


NICOTINE IN SULPHURETTED HYDROGEN. 






66-7 2-0 
14-3 -57 
6-67 -40 
4-00 -64 


2-67 
2-56 


2-27 
1-92 
1-03 


86 
96 
79 


1-96 
1-84 
0-81 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 



159 




o i 



Fig. 1. 

(1) Acctiimide in hydrogen bromide. 

(2) Tetramethylammonium bromide in hydrogen bromide. 

(3) iodide 

(4) Acetonitrile in hydrogen chloride. 

(5) Tetramethylammonium chloride in hydrogen sulphide. 

(6) Acetamide in hydrogen chloride. 

(7) Triethylammonium chloride in hydrogen chloride. 

(8) Tetramethylammonium chloride in hydrogen bromide. 

(9) Hydrocyanic acid in hydrogen chloride. 

(10) Ether in hydrogen chloride. 

(11) Triethylammonium bromide in hydrogen bromide. 

(12) Orthonitrotoluol in hydrogen bromide. 

(13) Piperidine in hydrogen sulphide. 



160 



DR. B. D. STEELE, DE. D. McINTOSH AND DR. E. H. ARCHIBALD 



5* 

i 




10 



V 

Fig. 2. 

(1) Triethylammonium chloride in hydrogen iodide. 

(2) Nicotine in hydrogen sulphide. 

(3) Ether in hydrogen iodide. 

(4) Triethylammonium chloride in hydrogen sulphide. 

(5) Ethyl benzoate in hydrogen iodide. 

(6) Acetone in hydrogen bromide. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 
Fig. 3 contains typical curves showing the variation of *V = p. with V for 

(1) Substances dissolved in halogen hydrides ; 

(2) Potassium chloride in water ; 

(3) Sodium carbonate in water ; 

(4) A solution of ammonia in water. 



161 






10 I? 14 16 

I/ 



18 ?0 



Fig. 3. 



The similarity between the variation with dilution of /cV 2 (or /cV") for solutions in 
the halogen hydrides and that of :V = p. for aqueous solutions is at once apparent. 

Since in the former case *V 2 = K', and in the latter p. = /cV = /*, and since 
both p.^ and K' are constants, it is evident that both sets of curves represent a 
variation in a and that K' represents the value of the molecular conductivity at 
infinite dilution of the electrolytic compound. 

Although the majority of the curves in figs. 1 and 2 are analogous to those for 
water solutions, some of them exhibit a maximum value for /cV", whilst others are 
extremely steep, thus indicating a very rapid increase in the value of . 

These irregularities are to be expected, since, as already stated, we have been 

VOL. CCV. A. Y 



162 DB. B. D. STEELE, DE. D. McINTOSH AND DE. E. H. AECHIBALD 

compelled to use, in the calculation of *V", the total concentration instead of that of 
the unassociated substance. 

It is also possible that more than one type of electrolytic compound is formed in a 
given solution, as, for example, the compounds ABCD and (AB) 2 CD ; in which 
case the total conductivity will be the sum of the conductivities due to the ionisation 
of each of these compounds. In such a case as this extremely complicated curves 
might result. Moreover, we cannot strictly apply the equation to the concentrated 
solutions, since for these the active mass (b) of the solvent is no longer constant. 

The fact that the curves, as a whole, are so analogous to those for a simple 
electrolyte in aqueous solution appears to indicate that, as a general rule, the main 
effect is due to the ionisation of a single substance. 

The equation :V" = aK' should also be applicable to abnormal solutions in other 
solvents. This is the case for the solutions investigated by PLOTNIKOFF (' Zeit. Phys. 
('hem.,' 1904, 48, p. 224), who found very abnormal variations of /u, for antimony 
tribromide and phosphorus pentabromide in bromine. The experimental figures for 
antimony tribromide lead to the following values for V and /cV" : 



V 

KV 3 


251, 

154, 


312, 
178, 


356, 

171, 


418, 
174, 


445, 
164, 


552, 

98, 


918 
168 

! 



The molecular conductivity of phosphorus pentabromide in bromine varies so 
irregularly as to suggest that some disturbing effect is at work rendering the figures 
valueless. 

Another solvent in which p. increases with concentration is amylamine (KAHLEN- 
BERG and HUHOFF, ' Jour. Phys. Chem.,' 1903, 7, p. 254), and the equation has been 
applied to the measurements of conductivity for cadmium iodide, ferric chloride 
and silver nitrate dissolved in this solvent. The results of the calculations when 
n = 2, 3 and 4 are given in Table III. It will be noticed that maxima are shown in 
each case. 

Passing on now to the consideration of the molecular weight determinations which 
are recorded in Part II., we find that some of these afford confirmation of our 
hypothesis, inasmuch as ether and acetone in dilute solutions possess a greater 
molecular weight than the theoretical. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 

TABLE III. 



163 



V. 


*V. 


*V 2 . 


K-V 3 . 




SILVER NITRATE 


IN AMYLAMINE. 


4001 


530 


212 


0-085 


4351 


639 


278 


0-121 


5096 


870 


443 


0-226 


6206 


1-128 


700 


0-434 


8629 


1-402 


1-21 


0-021 


1-158 


1-476 


1-71 


1-98 


1-685 


1-376 


2-32 


3-91 


2-302 


1-144 


2-63 


6-06 


2-850 


0-908 


2-59 


7-37 


3-261 


0-744 


2-43 7-91 


6-330 


0-168 


1-06 


6 73 


11-45 


0-038 0-44 


4-98 


31-07 


0-008 0-24 


7-72 


81-63 


0-002 0-16 


1 33 


CADMIUM IODIDE IN AMYLAMINE. 


0-7810 -465 


363 


284 


8909 


534 


476 


424 


1-095 


542 


594 


650 


1-237 


480 


594 


735 


1-450 


346 


502 


728 


1-738 


0-187 


325 


565 


2-473 


0-034 


084 


208 


5-482 


0-002 


Oil 


055 




V. A. AV. 


FERRIC CHLORIDE IN AMYLAMINE. 


5-021 0-217 1 09 


13-43 0-158 2-12 


18-34 0-138 2-53 


27-05 0-086 2-32 



We have been unable to ascertain whether the molecular weight reaches a limiting 
value with dilution, as the experimental errors incidental to measurements at the low 
temperatures involved prevented the examination of the more dilute solutions. 

KAHLENBERG, WALDEN, and others have called attention to many solutions in 
which, although p. varies normally, the solute is associated. 

Y 2 



164 DE. B. D. STEELE, DR. D. McINTOSH AND DR. E. H. ARCHIBALD 

Thus WALDEN and CENTNERSZWER ( 'Zeit. Phys. Chem.,' 1902, 39, p. 513) found 
that the molecular weight of potassium iodide dissolved in hydrocyanic acid is twice 
as large as the normal. ABEGG ('Die Theorie der electrolytischen Dissociation,' 
p. 103) has pointed out that this can be explained by the assumption that the 
undissociated substance is polymerised ; in which case a high average molecular 
weight might occur even with considerable ionisation. 

A compound such as (KI) 4 , for example, if it were completely dissociated into two 
ions, would have an average molecular weight of 332. We find that in most cases the 
molecular weight increases with increasing concentration, and although the opposite 
change occurs in dilute aqueous solution, this variation is the same as that which 
takes place in more concentrated aqueous solutions. 

This will be seen from the following comparison of the figures for acetone dissolved 
in hydrogen bromide with those for lithium bromide dissolved in water, the latter 
figures being taken from a recent paper by JOXES and GETMAN ('Zeit. Phys. Chem.,' 
1904, 49, p. 390). 

(a) Acetone in hydrogen bromide 

c = concentration in gram-molecules per litre = 0'51, 1'17, 1'85, 2'5G ; 

- = molecular depression = 4 '5, 4 '5, G'5, 11 '5. 

C- 

(&) Lithium bromide in water 

c = 0'48, 0-97, 1-94, 3'88 ; A = 4'07, 4'41, 5'31, 7'86. 

JONES and GETMAN attribute the apparent increase in the number of molecules in 
more concentrated solution to the formation of hydrates in solution. 

The low molecular weight which we have found for triethylammoniam chloride in 
sulphuretted hydrogen, although at first sight difficult to reconcile with the hypothesis 
of association, is not inconsistent with it. 

Thus if the compound formation and subsequent dissociation takes place according 
to the general scheme 

nAB+mCD ^ (AB),, (CD) W 
and mj .0 

(AB), (CD) m (AB),, (CD) m +mD, 

and if dissociation were nearly complete, it is evident that if m is equal to or greater 
than n, a larger number of molecules than n would be formed, and therefore the 
average would be less than the theoretical molecular weight. 

We can offer no suggestion as to why toluene, when dissolved in hydrogen chloride, 
although it absolutely fails to conduct the current, possesses such an extremely low 
molecular weight. Similar cases have been observed by KAHLENBERG, but no 
explanation has been suggested. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 165 

A possible explanation of the abnormal variation of molecular conductivity might 
be found in the hypothesis that when acetone or ether is added to hydrogen bromide 
the acetone or ether acts as an ionising solvent, and the hydrogen bromide is ionised. 
When looked at from this point of view, the variation of p. which actually occurs 
appears as a normal one. This explanation is, however, shown to be incorrect when 
we come to consider the transport number experiments. 

Thus, during the electrolysis of ether in hydrogen bromide, the deposition of 
1 gram-molecule of silver by the current is accompanied by a transport of - 8 gram- 
molecule of ether to the cathode. But, if the ether did not take part in the 
electrolysis, the same result would be obtained by the transport of a sufficient 
quantity of bromine as anion from the cathode to the anode. 

A simple calculation, however, shows that in order to bring this about no less than 
23 gram -molecules of bromine must be transported for every gram-molecule of silver. 

Now we have shown that FARADAY'S law is valid for solutions in hydrogen 
bromide, and accordingly we conclude that ether takes part in the carriage of the 
current, and that conduction is not due to ionisation of the hydrogen bromide. 

Information regarding the constitution of the electrolyte is also afforded by the 
transport number. If we again consider the case of ether dissolved in hydrogen 
bromide, there is in solution an electrolyte of the formula ((C 2 H 5 ) 2 0) 2 (HBr) n , which 
can ionise either 

+ 
(1) into H ions and a complex anion ((C 3 H 5 ) 2 0) 2 Br B 

or (2) Br cation ((C 2 H,) 2 O)oH. 

If the former, the ether will be transported to the anode as a component of a 
complex anion ; if the latter, it will be carried to the cathode as a component of a 
complex cation. Experiment has proved that the latter is the case not only for ether 
but also for the other substances which have been examined. 

It has been found that the cation transport number increases considerably with 
concentration. This increase can be easily explained if we assume, with JONES and 
GETMAN (loc. cit.), that the number of molecules of solvent in combination with one 
molecule of solute is greater in the more dilute solution. 

According to the theory of ABEGG and BODLANDER (' Zeit. fur Anorg. Chem.,' 
1899, 20, p. 453), the resulting change of constitution of the electrolyte would be 
conditioned as follows : 

Any salt in which one ion is much weaker than the other manifests a tendency to 
form complex ions by the addition of a neutral molecule to the weaker ion. In the 
solutions under discussion the weaker ion would undoubtedly be the complex cation, 
which, when the active mass of the solvent (neutral molecules) was increased by 
dilution, would tend to become still more complex by the addition of more solvent 
molecules. 



166 DE. B. D. STEELE, DE. D. McINTOSH AND DE. E. H. ARCHIBALD 

The effect of this increased complexity would be that the velocity of the ion would 
be diminished without altering the ionic change, and also that the concentration 
change at the cathode would be lessened, owing to the carriage of extra solvent 
molecules to the cathode. Both of these effects would cause a diminution of the 
cation transport number as the solution was diluted. 

It will be noticed that this explanation involves a change in the active mass of the 
solvent, and, as a matter of fact, it was not possible to measure the transport number 
except in solutions which were so concentrated, that the assumption of a constant 
active mass for the solvent was no longer justified. 

We have not been able to calculate, even approximately, the velocity of the various 
ions, as we had no means of determining the actual nature, concentration, or degree of 
dissociation of the corresponding electrolytes. 

Summary. 

The foregoing pages contain an account of measurements of the vapour pressures, 
densities, surface energies, and viscosities of the liquefied hydrides of chlorine, bromine, 
iodine, sulphur, and phosphorus. 

The solvent action of these substances has also been investigated, and we have 
shown that, with the exception of phosphuretted hydrogen, they are all able to act 
as ionising solvents, and the conductivity, molecular weight, and transport number of 
certain dissolved substances have been measured. 

The results of the measurements, although abnormal, are not inconsistent with the 
ionic theory ; since we have shown that 

(1) If in a given solution the electrolyte is a compound containing n molecules ot 
the dissolved substance, the concentration of this compound will be proportional to 
the n th power of the concentration of the dissolved substance, and therefore the 
expression for the molecular conductivity of the electrolyte becomes icV" instead of /cV. 
We have also shown that /cV" = aK', and therefore the molecular conductivity of the 
electrolyte increases with dilution in these solutions in the same manner as in aqueous 
solutions. 

The variation of the molecular conductivity of the electrolyte with dilution is 
probably complicated by the occurrence of compounds which contain a different 
number of solvent molecules at different dilutions. 

(2) The want of agreement between conductivity and cryoscopic measurements is 
a necessary consequence of the occurrence of polymers or compounds in solution, and 
may be taken as evidence of the existence of such compounds. 

(3) The conduction of organic substances when dissolved in the halogen hydrides 
is best explained by the occurrence of electrolytic compounds of the organic 
substance with the solvent. Transport number measurements have shown that the 
organic substance is carried to the cathode as a component of the complex cation. 



ON THE HALOGEN HYDRIDES AS CONDUCTING SOLVENTS. 167 

In conclusion, we wish to express our thanks to Professor B. J. HARRINGTON, 
Director of the McGill University Chemical Laboratory, and to Professor JOHN GIBSON, 
of the Heriot Watt College, for placing facilities at our disposal and for kindly 
interest taken in the work. Our thanks are also due to Professor JOHN Cox, 
Director of the McGill Physical Laboratory, for the use of apparatus, and for kindly 
supplying us with large quantities of liquid air. We also wish to express our thanks 
to the Research Grant Committee of the Chemical Society for a grant made to one 
of us, by means of which a large portion of the expense of the work of Part III. has 
been met. 



[ 169 ] 



V. The Atomic Weight of Chlorine: An Attempt to determine the Equivalent 
of Chlorine by Direct Burning with Hydrogen. 

By HAROLD B. DIXON, M.A., F.R.S. (late Fellotv of Balliol College, Oxford), 

Professor of Chemistry, and E. C. EDGAR, JB.Sc,, Dalton Scholar 

of the University of Manchester. 

Received May 18, Head May 18, 1905. 

CONTENTS. 
PART I. GENERAL. 

PART II. DETAILS OF EXPERIMENTS. 

Page 

1. Preparation of hydrogen 172 

2. The palladium bulb 175 

3. Preparation of chlorine 177 

4. The chlorine bulb 180 

5. Preparation of reagents 181 

6. Weighing the bulbs 185 

7. Method of carrying out the combustion 189 

8. Results of the experiments 195 

Appendix ... .198 

PART I.- GENERAL. 

SOME apology seems needed in presenting a new research on the atomic weight of an 
element already measured with a precision which the highest living critic has 
emphasised as " the magnificent accuracy of STAS' determination." 1 * Moreover, the 
present experiments cannot claim an accuracy to be compared with any individual 
series of STAS' ratios. But, on the other hand, STAS' atomic weight of chlorine is 
derived indirectly from oxygen by a series of operations which include the deter- 
mination of (1) the oxygen in potassium chlorate, (2) the silver equivalent to the 
molecule of potassium chloride, and (3) the composition of silver chloride. STAS 
himself has assigned different values to these ratios at different times ; e.g., in 1860 he 
found that 100 parts of silver were equal to 69'103 of potassium chloride, in 1882 he 

* F. W. CLARKE, 'A Recalculation of the Atomic Weights.' New edition. 1897, p. 57. 
VOL. CCV. A 391. Z 24.8.05 



170- PEOFESSOE H. B. DIXON AND ME. E. C. EDGAE 

found 100 of silver equal to 69'119, and in his latest work to 69'123 of potassium 
chloride. Therefore, although STAS' value 35'457 (0 = 16) is in satisfactory agreement 
with CLARKE'S value 35 '447 re-calculated from all the best determinations, it is 
possible that some constant error may occur in some part of the long chain connecting 
the value of hydrogen with that of chlorine, an error which would be repeated from 
link to link, and would become evident only when the two ends of the chain were 
connected up. 

A direct comparison between hydrogen and chlorine might not only serve to detect 
any systematic error in this chain of ratios, but such a comparison, inasmuch as it 
does not involve the probable error of other ratios, would be cceteris paribus more 
exact. Again, the closing of the chain between hydrogen and chlorine with 
reasonable accuracy would permit the accidental errors to be distributed and prevent 
their accumulation at the unconnected end. The accumulated "probable error" in 
CLARKE'S recalculated value for chlorine is '0048 ; the " probable error" of our nine 
experiments is '0019. 

The suggestion to carry out this work was made to us by Professor EDWARD W. 
MORLEY, who happened to visit our laboratories when pure chlorine was being 
prepared by the electrolysis of fused silver chloride. He suggested that we should 
burn weighed hydrogen and chlorine in a closed vessel, just as he had burnt weighed 
hydrogen and oxygen. After some discussion we decided to make the attempt an 
attempt which was rendered possible by the fact that one of us was enabled, by a 
research scholarship, to devote his whole time to the investigation. 

A year was spent in designing, making and testing the several parts of the 
apparatus. In the second year we put together the pieces and carried through 
preliminary experiments, which led to some modifications and further trials. In the 
third year the apparatus was got into Avorking order and the determinations made. 
After the three years' work we are painfully aware how far our attempt falls short of 
the precision of Professor MORLEY'S own determination, but the relation we have found 
between hydrogen and chlorine seems worthy of record on account of the directness 
of the method of comparison. 

Our method was, briefly, as follows : Chlorine prepared by the electrolysis of 
fused silver chloride (with purified carbon poles in a Jena-glass vessel) was condensed 
and weighed as a licpuid in a sealed glass bulb. This was attached to a vacuous 
" combustion globe " and the chlorine allowed to evaporate slowly .nto the globe. 
The hydrogen prepared by the electrolysis of barium hydrate was dried and absorbed 
by palladium in a weighed vessel. The palladium on being warmed gave off the 
hydrogen, which was ignited by a spark and burnt at a jet in the combustion globe 
previously filled with chlorine. The gases were regulated so as to maintain the 
hydrogen flame until nearly all the chlorine had been combined ; then the palladium 
was allowed to cool and the hydrogen was turned off just before the flame died out. 
The hydrogen chloride, as it was formed in the flame, was dissolved by water standing 



ON THE ATOMIC WEIGHT OF CHLORINE. 



171 



in the globe, which was kept cool by ice. A little hydrogen chloride was formed by 
the action of the water-vapour on the chlorine in the flame, a corresponding amount 
of oxygen being liberated. This oxygen was determined in the analysis of the 
residual gases, which contained, besides traces of air, the small quantity of hydrogen 
which filled the capillary tube between the tap and the jet when the flame was 
extinguished, and any that might escape unburnt from the flame. 

The chlorine remaining in the globe unburnt, as gas and in solution, was determined 
by breaking a thin glass bulb containing potassium iodide. The residual gases having 
been pumped out (and any iodine vapour caught by a wash-bottle), the liberated 
iodine was determined by standard thiosulphate in an atmosphere of carbonic acid. 
In calculating the unburnt chlorine from the iodine, the atomic weight of chlorine 
was assumed to be 35'195 and the atomic weight of iodine 126'015.* In each 
experiment we burnt about 11 litres of hydrogen and 11 litres of chlorine. The 
volume of chlorine left unburnt was about 2 per cent, of the volume burnt. 

The balance (by OERTLING) was fixed on a stone pedestal in an underground cellar. 
The vibrations of the pointer were read by a telescope, GAUSS' method of reversals 
being used. The chlorine and the hydrogen bulbs were counterpoised on the balance 
by bulbs of the same glass and of nearly the same displacement, and the small 
weights used in the weighings were reduced to a vacuum standard. 

In the following table are given the corrected weights of hydrogen and of chlorine 
burnt in the several experiments the weights of hydrogen being rounded off to 



1 milligramme : 



TABLE I. 





Hydrogen burnt, 


Chlorine burnt, 


Atomic Weight of 




in grammes. 


in grammes. 


Chlorine. 


1 


9993 


35-1666 


35-191 


2 


1-0218 


35-9621 


35-195 


3 


9960 


35-0662 


35-207 


4 


1-0243 


36-0403 


35-185 


5 


1-0060 


35-4144 


35-203 


6 


988V 


34-8005 


35-198 


7 


1-0159 


35-7639 


35-204 


8 


1-1134 


39-1736 


35-184 


9 


1-0132 


35-6527 


35-188 


Mean .... 


35-195 -0019 



In the whole of these experiments 9'1786 grammes of hydrogen combined with 
323 "0403 grammes of chlorine ; hence the atomic weight of chlorine, calculated in mass, 
is 35-195. 

* G. P. BAXTER, 'Proc. Amer. Acad.,' xl., 419. 
z 2 



172 PKOFESSOK H. B. DIXON AND ME. E. C. EDGAR 

The percentage composition of hydrochloric acid according to these deter- 
minations is : 

Chlorine 97-237 

Hydrogen 2 -763 

100-000 

The number we have obtained for the atomic weight of chlorine is appreciably 
hio-her than that calculated by F. W. CLARKE from the previous determinations, and 
is slightly higher than STAS' value : 



CLARKE'S calculation. 


STAS. 


Dixox and EDGAR. 




35-179 


35-189 


35-195 


H = l 


35-447 


35 '457 


35-463 


= 16 



After our experiments were completed, we heard that Professor T. W. RICHARDS 
was engaged on a revision of STAS' work on the composition of silver chloride. 
G. P. BAXTER quotes the value 35 '467 as having been obtained by RICHARDS and 
WELLS for the atomic weight of chlorine, a number slightly higher than our own.* 

It would not be difficult to extend our experiments, using larger quantities of the 
gases, if in the judgment of chemists it were thought desirable, t 



PART II. -DETAILS OF EXPERIMENTS. 
1. Preparation of Hydrogen. 

For the preparation of hydrogen we employed the electrolysis of a solution of 
barium hydrate, first proposed by BRERETON BAKER,! as a means f preparing 
hydrogen free from traces of hydro-carbons. 

Since barium carbonate is quite insoluble in a solution of barium hydrate, any 
slight action of the carbonic acid of the air ' on the dissolved hydrate during its 
unavoidable exposure while filling the electrolytic apparatus might be safely neglected. 
We have to thank Mr. BRERETON BAKER for kindly supplying us with some of his 
highly purified barium hydrate. It had been re-crystallised fifteen times and was not 
radio-active. It still contained a very small trace of barium carbonate. 

The arrangement of the hydrogen apparatus is shown in fig. 1. Three preliminary 

* Professor RICHARDS writes (February 13, 1905) that he finds 100.00Q parts of silver yield 132,867 of 
silver chloride, whereas STAS considered 132,850 the most probable result. This new determination, 
combined with our value for chlorine, would give silver an atomic weight 107 '90. 

t As further experiments have shown that chlorine can conveniently be burnt in an atmosphere of 
hydrogen, one of us proposes to make a fresh set of determinations in this way and to condense and 
weigh the hydrochloric acid formed. July, 1905. 

I ' Jl. Chem. Soc.,' 1902, vol. 81, p. 400. 



ON THE ATOMIC WEIGHT OF CHLORINE. 



173 




C-maEi.'..:i4&?='-?w>j&?i6 
S23^23SSEngEj 



1 

tf\ 

I 

" 




I 



bo 

S 



174 PEOFESSOR H. B. DIXON AND MR. E. C. EDGAR 

drying tubes were employed, each 1 metre in length and 2 '5 centims. in diameter, 
filled with small pieces of purified potassium hydrate. The gas then passed through 
a U-tube containing platinised pumice, kept at a temperature of 220 C., in order to 
remove any oxygen diffusing from the + electrode, and then through a short 
horizontal tube and three long U -tubes filled with pure phosphorus pentoxide. As 
recommended by COOKE, the phosphorus pentoxide was packed closely into the 
drying tubes and was alternated at frequent intervals with plugs of clean glass-wool. 
To ensure efficient drying, the current of hydrogen was passed through these drying 
tubes at a rate not greater than 2 litres an hour. At the end of our experiments the 
last layers of phosphorus pentoxide had picked up so little moisture that a slight 
tapping of the tube threw the powder into a cloud. 

The drying tubes, when filled, were fused together, and to the last phosphorus 
pentoxide tube was fused the tap C. This, in turn, was fused to one limb of a 
T-piece, to the other two limbs of which were fused the bulb containing the palladium 
foil and the Toepler pump. To the first potassium hydrate drying tube at the other 
end of the apparatus was fused a three-way tap. The U-tube E. in which the 
electrolysis of barium hydrate was carried out, was also fused to D, whilst the third 
arm of D opened into the air. 

When the current was passed through the warm barium-hydrate solution between 
the platinum electrodes G and G,, the evolved gases were allowed to escape into the 
atmosphere until the air, which was originally contained in the two arms of the 
U-tube, had been replaced by hydrogen and oxygen respectively. Connection with 
the atmosphere was then cut oft' by closing the tap H and by fusing off the capillary 
portion of the opening F. During our experiments the solution showed no signs of 
milkiness and no precipitate settled at the bottom of the tube ; we believe, therefore, 
that no carbonate was present. 

The preparation and occlusion of hydrogen was carried out as follows : Before the 
fusion of the palladium bulb to the apparatus, the tubes on the right-hand side of the 
tap D were exhausted as far as possible by means of the pump. The U-tube, 
containing the solution of barium hydrate, was raised to a temperature of 60 C. in a 
water-bath (in order to dissolve the hydrate which had crystallised out from the 
solution) and the electrolysis commenced. The evolved oxygen escaped into the air 
through the tap H and the tube K, filled with a dried mixture of CaO and Na 2 SO 4 , 
while the hydrogen was admitted, by very cautiously opening the tap D, to the 
evacuated part of the apparatus. The stream of hydrogen was continued until the 
bubbling of the gas through the manometer tube showed that the previously evacuated 
portion of the apparatus was now full. The electrolysis was discontinued, the tap D 
closed and the drying tubes again evacuated. This operation of filling and exhausting 
was repeated twelve times in order to get rid of all traces of air. The taps C and D 
were then closed and the electrolysis stopped. 

The bulb A containing the thin palladium foil was then fused to the apparatus. 



ON THE ATOMIC WEIGHT OF CHLOEINE. 175 

The palladium was raised to a very low red heat and the apparatus on the right-hand 
side of the tap C evacuated, arid then allowed to cool to the ordinary temperature. 
The tap C was cautiously opened, the electrolysis resumed, and hydrogen admitted to 
the palladium until it was saturated, care being taken that the pressure on the left- 
hand side of the tap C was always kept slightly above the atmospheric. This last 
precaution was easily effected by opening the tap D fully and regulating the admission 
of the gas to the palladium by means of the tap C. C was now closed, the temperature 
raised to a very low red heat, and the evolved gas sucked out by the pump. The 
operation of alternately filling the palladium with hydrogen and evacuating the bulb 
at a high temperature was repeated four times, when it was considered that all traces 
of nitrogen or other gases had been removed from the palladium bulb and the 
connecting tubes on the right-hand side of C. The palladium after the final 
exhaustion was maintained at a low red heat whilst hydrogen was admitted to it 
through C. 

When the pressure throughout the apparatus had become a little more than 
atmospheric this was easily attained by so adjusting the tap H of the electrolysis 
tube that the rate of escape of the evolved oxygen through it was slightly less than 
its actual rate of evolution the tap B was slightly opened and the current of 
hydrogen was passed through the palladium, the gas finally escaping through a 
capillary tube dipping under mercury. The palladium was now allowed to cool very 
slowly, the current of hydrogen passing through it all the time. Great care was 
taken that the rate of entry of hydrogen to the palladium was always greater than 
its rate of occlusion, or, in other words, that an excess of hydrogen was constantly 
escaping through the capillary tubing during the occlusion. 

At the temperature of maximum absorption of hydrogen from 07 to 100 C., the 
cooling of the palladium was interrupted and the temperature kept constant for 
one hour. The cooling was then allowed to continue, hydrogen passing through the 
apparatus all the while, until the temperature of the room was reached. The 
taps B, C, D, and H were then finally closed and the electrolysis discontinued. The 
palladium bulb was fused off from the rest of the apparatus, the outside cleaned and 
dried, and the whole was then ready for weighing. 

2. The Palladium Bull}. 

The palladium vessel A (fig. 2) was a bulb of hard Jena glass of about 180 cub. 
centims. capacity, fitted on the one side with a tap B, the inner portion of a ground 
glass joint M, and a glass jet J, at which the combustion of hydrogen in chlorine 
was carried out ; and on the other with a capillary tube by which it could be 
attached to the rest of the hydrogen apparatus and afterwards separated by fusion 
with the blowpipe flame. 

Since the date when Professor E. W. MOELEY defined a tap as "a contrivance for 



176 



PKOFESSOR H. B. DIXON AND MR. E. C. EDGAR 



lessening the flow of -gas through a tube," improvements have been made which 
seemed to us to justify the use of one for regulating the flow of hydrogen from the 
palladium bulb. The tap B, fig. 2, was made with a long barrel with its bearings 




B 



Fig 2. The palladium vessel. 

ground to the sheath for a length of 30 millims. The barrel forms a portion of an 
elongated cone, its diameter at the wider end being 10 millims., and at the narrower 
end 8 millims. The bore of the tap is inclined so that one opening is 10 millims. 
above the other. The sheath of the tap ends in a closed bulb below and a cup 
above. 

The method of lubricating and fixing the tap was as follows : After thorough 
cleaning and drying, the bulb b of the tap was filled with dry mercury to such a 
height that the barrel of the tap, when placed in position, just touched its surface. 
The mercury was then gently heated until it filled the whole bulb. The lubricant 
glacial phosphoric acid was melted and carefully rubbed over the barrel, which was 
placed in position, turned several times to ensure equal distribution of the lubricant, 
and then pressed firmly into the sheath whilst the bulb b containing the mercury 
was cooled. The bulb now contained no air, but the cooling resulted in the 
production of a partial vacuum, which kept the tap firmly fixed. We have tested 
this tap by a pump and found it to remain perfectly gas-tight. All the other taps 
used in the apparatus with the exception of the chlorine tap were made and used 
in the same way. We are indebted to the skill of the University glass-blower, 
OTTO BAUMBACH, for the accurate grinding of these taps, and for the joints by 
which he succeeded in fusing hard Jena to soft glass. 

It was of course essential that the weight of the palladium bulb should be most 
accurately determined before and after the combustion of its charge of hydrogen. 
To avoid change of volume the bulb was made of a hard Jena glass which 
preliminary hydrostatic weighings showed not to alter when heated to dull redness 
and cooled. The charged palladium bulb was heated and cooled alternately to 



ON THE ATOMIC WEIGHT OF CHLORINE. 177 

determine its change of volume, if any. When immersed in water to a mark on the 
stem the bulb weighed 

Before heating 230-314 grammes. 

After heating for two hours to a dull red heat .... 230 '311 

After a second heating 230-307 

After a third heating 230-308 

The alteration in volume of the bulb, after heating to dull redness, was there- 
fore so slight that the difference in its displacement of air was negligible. In the 
actual experiments the bulb was never heated beyond 550 C. 

The palladium was used in the form of thin foil. We are indebted to Messrs. 
JOHNSON and MATTHEY for kindly supplementing our stock for the purpose of this 
investigation. The bulb contained sufficient palladium foil (360 grammes) to absorb 
about li grammes of hydrogen. When the bulb A had been detached from the rest 
of the hydrogen apparatus and had been cleaned, it was suspended by platinum wire 
from one arm of the balance, from the other was suspended a counterpoise (of the 
same Jena glass) which had nearly the same displacement as the palladium bulb. 
It was then weighed by GAUSS' method of reversals. The balance case, after each 
reversal, remained closed at least half-an-hour before a new weighing was started. 
The air displaced by the small weights added to secure equilibrium was allowed for. 
By equalising the volumes of the systems suspended from the arms of the balance, 
errors due to variations of temperature in the balance case and to any deposition of 
moisture on the bulb were avoided. 

3. Preparation of Chlorine. 

SHENSTONE,* in 1893, first proposed the electrolysis of fused silver chloride in a 
vacuum as the best means of obtaining pure chlorine. He stated that his chief 
difficulty was the rapid formation of silver trees, which eventually made contact 
between the electrodes and thus prevented any further decomposition of the fused 
chloride. In 1901, MELLOR and KussELLf substituted for SHENSTONE'S tube a V-tube 
of the hardest Jena glass, so that the silver tree had to travel along the two limbs of 
the V before making contact, and thus the decomposition of silver chloride could be 
carried on to a greater extent than in SHENSTONE'S apparatus. They fastened their 
carbons to glass tubes (ground into the necks of the V) by means of a plaster of Paris 
joint. 

We have modified their apparatus by drawing out the upper portion of each arm of 
the U, and melting it on to the carbon electrode for a length of about 2 - 5 centims. 
We fused a little silver chloride round the top junction of glass and carbon. A 
mercury cup completed the joint, and served for making electrical contact with the 
carbon. Such a joint, even with a vacuum in the interior of the tubing, is quite 

impervious. 

* ' Journ. Chem. Soc.,' 71, 471 (1897). 

t 'Journ. Chem. Soc.,' 82, 1272 (1902). 
VOL. CCV. A. 2 A 



178 PROFESSOR H. B. DIXON AND MR. E. C. EDGAR 

The arrangement of the apparatus is shown in fig. 3. A was the U-tube of Jena 
glass, having two delivery tubes B and B t which united at C ; its capacity was such 
as to'admit of the fusion of 800 grammes of silver chloride introduced through the 
side tube F. The carbon electrodes D and D 1} of 2 millims. diameter, were specially 
made for us by the Acheson Graphite Company, Niagara. Before being fixed in 
position they were heated to redness for twelve hours in a current of chlorine, and 




Fig. 3. Chlorine apparatus. 

were then kept in vacuo in a porcelain tube for three hours at a bright red heat. 
A special glass joint at G permitted the junction of the U-tube to the other portion 
of the apparatus, which was constructed of soft glass. This joint was made by fusing 
together a series of twelve very short pieces of tubing which varied by small 
gradations from hard Jena to soft glass. H was a small drying tube containing pure 
phosphorus pentoxide, which was kept in position by two plugs of clean glass-wool. 
K was a glass tube (capacity 25 cub. centime.) in which a sample of the prepared 
chlorine could be collected to test its purity. L was a T-piece, one limb of which 
was fused to the chlorine generator ; another led, via the absorption tubes M and N, 
to the mercury pump, whilst the third was fused to the " chlorine bulb." 

To prevent any residual chlorine reaching the pump, it was passed through the 
tube M (which could be filled with mercury to a suitable height by raising a 
reservoir), and then through a tube N, 1 metre in length and 4 centims. in diameter, 
packed closely with pure potassium hydrate. A little mercury, contained in the 
cavity 0, acted as a tenioin. The dulling of its bright surface would have indicated 



ON THE ATOMIC WEIGHT OF CHLORINE. 179 

that the absorption of chlorine had not been complete, but, at the end of our 
experiments, its lustre was unimpaired. 

Preparation of Silver Chloride. Commercial silver nitrate was purified by re-crys- 
tallisation twice from water. A strong solution of hydrochloric acid was prepared by 
cautiously distilling the pure concentrated acid, washing the evolved gas with a little 
water and then dissolving it in re-distilled water, kept cool by means of an ice and 
salt freezing mixture. 

A strong solution of re-crystallised sodium chloride was prepared, and into it was 
passed the acid gas evolved by heating the solution of hydrochloric acid previously 
made. The precipitated sodium chloride was washed with a little ice-cold water, 
dissolved in fresh re-distilled water and again re-precipitated by means of hydrochloric 
acid gas. This re-precipitation was carried out three times. Silver chloride was 
then prepared by adding a dilute solution of the re-crystallised silver nitrate to excess 
of a dilute solution of the purified sodium chloride. 

The precipitation of the silver" chloride and all subsequent operations were carried 
out in the absence (as far as possible) of actinic light. The supernatant liquors were 
decanted as soon as possible and the silver chloride washed repeatedly with boiling 
distilled water, until a test portion of the washings gave no cloudiness with silver 
nitrate. The silver chloride was then frequently agitated with more hot distilled 
water and allowed to stand in contact with it for some time. Then the final washings 
were decanted and the silver chloride was dried as completely as possible in large 
porcelain dishes on a water-bath. It was then cautiously fused in deep porcelain 
crucibles and kept in the molten state for twenty-four hours, care being taken to 
prevent contact, during the prolonged heating, between the acid gases of the flame 
and the molten chloride. The chloride was then poured into a clean silver trough so 
as to form thin sheets. These, on cooling, were easily detachable, and were cut into 
small fragments. The silver chloride prepared in this way was a colourless, horn-like, 
translucent substance, which could be easily broken or cut into small pieces. 

The operation of fusing the requisite amount of silver chloride in the U-tube A 
was carried out as follows: The U-tube (filled through the side tube F with the 
solid pieces of silver chloride up to the level of the carbon electrodes) was gradually 
raised in temperature by heating the cast-iron box in which it was closely packed 
round with asbestos. A high-range thermometer, with its bulb resting on the bend 
of the U-tube, indicated the temperature of the chloride. When the contained silver 
chloride had fused, more was slowly added until the calculated amount, 800 grammes, 
had been completely reduced to the molten state. The side tube F was then sealed 
and the whole apparatus was exhausted by the pump. When the tubes were 
thoroughly evacuated the tap P was closed, and the current from one storage cell 
was passed through the silver chloride for a short time. The current was then 
increased by the addition of another cell, and chlorine was steadily evolved until the 
whole of the apparatus on the left-hand side of the tap was filled with chlorine at a 

2 A 2 



PKOFESSOE H. B. DIXON AND ME. E. C. EDGAR 

pressure slightly above atmospheric. Then the current was discontinued, the tap P 
cautiously opened, and the gas allowed to escape, first through mercury contained in 
the tube M and then through solid potassium hydrate. Any gas other than chlorine 
was then sucked out by the automatic pump, which, during 'the first part of the 
electrolysis, was kept constantly working. 

The operation of filling the apparatus with chlorine and exhausting was repeated 
four times. The gas from the first two fillings was not completely absorbed. In 
preparing chlorine for our determinations we filled the apparatus five times, and tested 
the fifth by fusing-off the side tube K and opening it under mercury. The absorption 
was so complete as to leave no visible gas residue. This test assured us that no air 
was left in our chlorine. The fact that the chlorine first evolved was allowed to 
escape was a safeguard against the possible presence of bromine or iodine, for any 
bromide in the silver chloride would have been decomposed by the chlorine, and the 
evolved bromine would have been carried over with the chlorine first escaping. 

The chlorine bulb (immersed in a cooling mixture of solid carbonic acid and ether 
contained in a silvered Dewar tube) was then filled with liquid chlorine. The current 
was increased and the condensation allowed to proceed until the liquid reached the 
level of a circular line etched on the bulb, when the current was stopped. About 
37 grammes of liquid chlorine were collected in each experiment. Finally the 
chlorine bulb was separated by fusion. 

Irregularities, arising in the electrolytic cell, were shown by an ammeter placed 
in the electrical circuit. We found it advisable, as SHENSTONE says, to prevent these 
irregularities by frequently reversing the current for a short interval of time, thus 
shattering any incipient silver tree. 

4. The Chlorine Bulb. 

Chlorine, prepared by the electrolysis of fused silver chloride in vacuo, and dried 
by phosphorus pentoxide, was condensed by means of a freezing mixture of solid 
carbonic acid and ether, or by liquid air, in an apparatus shown in fig. 4. The 
chlorine vessel, which was made of soft glass, consisted of a stout glass bulb, A, 
holding about 40 cub. centims. To this was attached one limb of a T-piece, made 
of capillary tubing ; another limb could be fused to the source of chlorine, whilst the 
third ended in a cul-de-sac (B). 

B was a contrivance by means of which we got over a difficulty, which threatened 
at one time to bring our work to a premature end. For a long time we were unable 
to discover any means by which liquid chlorine could be safely weighed, and, at 
the same time, be under such complete control as to admit of its subsequent regular 
entry to the combustion globe. The pressure of liquid chlorine at ordinary 
temperatures is from 6 to 8 atmospheres, and the difficulties of successfully controlling 
such a pressure by means of a tap were found very great. 






ON THE ATOMIC WEIGHT OF CHLORINE. 



181 




After many failures we finally designed the vessel shown in fig. 4. The chlorine 
weighed in the bulb A could only reach the tap when the sealed end of the inner 
tube B was broken off by the rod of glass C falling on it. The tap D was an 
inversion of the ordinary form of tap, that 
is, its smallest diameter is at the top of 
the tap ; so that instead of the key having 
to be pushed into its socket, it has to be 
pulled into it to fit. Internal pressure, 
instead of tending to loosen the key, only 
made it fit more tightly. Of course, if 
the internal pressure became too great, the 
key was so firmly driven into its socket 
that it stuck, and then became useless. 
However, the taps we used, when lubri- 
cated with viscid phosphoric acid, with- 
stood a pressure of four atmospheres 
without sticking. Their chief disadvan- 
tages lay in the difficulties of cleaning and 
lubricating them, and in the fact that it 
was necessary to affix to them weights, 
suspended from a pulley, when carrying 
out exhaustions of vessels to which they 
were attached. We are not .aware that such taps have been used before in 
scientific research work ; they were made for us by the University glass-blower. 

The small space E (less than - 5 cub. centim.) immediately below the key of the 
special tap D, and the glass tubes connected with it, were first evacuated and then 
filled with pure chlorine from the silver chloride through the tube F, which was 
sealed off while the apparatus was cooled by immersion in a freezing mixture. On 
the removal of the freezing mixture, the gas trapped between E and F (about 4 cub. 
centims.) tended to expand, and thus held the tap D firmly in position. 

The chlorine condensation bulb, filled with approximately 37 grammes of liquid 
chlorine, was weighed in a precisely similar manner to that detailed for the palladium 
bulb. 

5. Preparation of Reagents. 

Iodine. Pure iodine was prepared by the first of the two methods proposed by 
STAS. A strong solution of potassium iodide was saturated with resublimed 
commercial iodine. To this, sufficient water was added to precipitate one half of the 
dissolved iodine. The supernatant liquid was decanted and the precipitated iodine 
repeatedly washed with small quantities of distilled water. It was then divided 
into two portions. The iodine, in the first, was distilled in steam, the solid distillate 



Fig. 4. Chlorine bulb. 



182 PEOFESSOR H. B. DIXON AND MR. E. C. EDGAR 

collected and dried in vacua over solid calcium nitrate, which was frequently 
changed. The iodine was then intimately mixed with 5 per cent, of its weight of 
purified barium oxide, and distilled to remove the last traces of water and hydrogen 
iodide. The wet iodine, in the second portion, was dissolved in a strong, cold 
solution of purified potassium hydrate until the solution had acquired a per- 
manent light yellow tinge. The solution was then evaporated to dryness on 
a water bath. The mixture of potassium iodide and iodate so obtained was 
then placed in a large platinum crucible, fitted with a platinum hood, and 
heated to dull redness for six hours. The resultant potassium iodide was re- 
crystallised five times from water and dried in vacuo over calcium nitrate, which 
was frequently changed. It was pure white in colour, and contained no trace of 
potassium iodate ; its solution in water was neutral and remained colourless when 

exposed to light. 

Standard Solution of Iodine in Potassium Iodide. In a small weighing bottle, 
carefully cleaned and dried, iodine, purified as described, was placed. This was 
kept in a desiccator until ready for weighing. The details of the weighing are given 
below : 

Temperature at start 16'5 C., Barometer at start 759 -8 millims., 

Temperature at end, 15'5 C., Barometer at end 757 '0 millims., 

Weight of bottle and iodine 52-28137 grammes. 

Weight of bottle 23-70084 



28-58053 
Vacuum correction + -00279 



28-58332 

The weight of iodine dissolved was therefore 28 '58332 grammes. 

This iodine having been dissolved in a solution of potassium iodide, the iodine 
solution was brought into a 2-litre flask through a drawn out funnel, and the residual 
solution carefully washed in. 

The flask was calibrated by means of a burette previously calibrated, the neck of 
the flask being drawn out in the blowpipe flame. After cleaning and drying, the 
flask was filled with pure water from the burette, at the same temperature as that at 
which the burette had been calibrated. The last drops were allowed to run into the 
flask by contact with the glass surface immediately above the water, which stood in 
the constricted part of the neck. A circular line was etched on the glass to mark 
the exact level of the liquid in the constriction. 

The iodine solution was brought up to the etched mark by slowly adding pure 
water, the solution being shaken after each addition of water. The final tempera- 
ture of the solution was almost identical with the temperature at which the volume 



ON THE ATOMIC WEIGHT OF CHLORINE. 183 

of the 2-litre flask was determined. It was assumed that no loss in weight of the 
iodine had occurred during its solution in the potassium iodide solution. We had 
then 28'58332 grammes of iodine dissoved in 2033'68 of our units of volume, which 
gives '014055 gramme of iodine in one of our units of volumes. The solution was 
kept in the tightly stoppered 2 -litre flask. 

Potassium Hydrate. Potassium hydrogen carbonate was twice re-crystallised from 
water. The crystals were heated in a platinum crucible, fitted with a platinum hood, 
to a dull red heat for six hours. The potassium carbonate so obtained was dissolved 
in water, and silver carbonate added, and the mixture thoroughly agitated for 
three hours. The precipitate, composed chiefly of silver carbonate but probably 
containing traces of silver chloride and other substances, was allowed to settle and 
the supernatant liquid filtered into a silver dish through a filter filled with clean 
pieces of broken marble. 

The solution in the silver dish contained one part of potassium carbonate in twelve 
of water. It was heated to the boiling-point, and two parts of lime (prepared by 
heating calcium carbonate to bright redness in a platinum crucible, and previously 
slaked in ten parts of water) were added by degrees, the liquid being boiled for a few 
minutes after each addition of lime to ensure its complete conversion into calcium 
carbonate. The addition of lime completed, the solution was boiled for half-an-hour 
and allowed to clarify by standing. The clarified solution was then filtered through 
another marble filter into a silver dish and boiled down until the hydrate commenced 
to evaporate. The semi-solid mass was then poured into a silver dish and allowed to 
cool in vaauo over calcium chloride. It was then divided into four portions, the first 
was broken into small fragments and introduced as rapidly as possible into the potash 
drying tubes ; the second was broken into larger pieces with which the chlorine 
absorption tube (fig. 3) was filled ; the third was dissolved in pure distilled water 
and the solution employed in the preparation of potassium iodide, whilst the remainder 
was used in the purification of water. 

Pure Water. The water used in these experiments was prepared by rectifying hot 
distilled water from the laboratory still. This was distilled over potassium hydrate 
(purified as described) and potassium' permanganate, twice re-crystallised from water. 
The retort employed was made of hard Bohemian glass, the condensing tube and 
receiver of Gerate glass. Immediately before use these were cleaned and steamed. 
100 cub. centims. of this water, when slowly evaporated in a small platinum retort, 
gave no solid residue. 

Phosphorus Pentoxide. KAHLBAUM'S purest pentoxide, contained in Jena hard 
glass tubes, was distilled, at a bright red heat, in a current of pure dry oxygen 
through spongy platinum, kept in position by two platinised asbestos plugs. The 
distilled oxide condensed as a fine white crystalline powder in the cooler part of the 
Jena-glass tubes. It was kept in a tightly stoppered bottle until its introduction 
into the drying tubes. It answered all the tests recommended by SHENSTONE and 



PROFESSOR H. B. DIXON AND MR. E. C. EDGAR 

BECK for the identification of pure phosphorus pentoxide : (l) it did not reduce a 
10-per cent, solution of silver nitrate; (2) it did not reduce mercuric chloride when 
boiled with it ; and (3) on evaporating an aqueous solution of it to dryness and 
igniting moderately, no odour of phosphine was detected. 

Palladium Foil. The palladium, which was used in the form of thin foil cut into 
very small pieces, was heated to dull redness in a current of pure dry air for twenty- 
four hours, in order to eliminate any grease which might have been acquired during 
rolling. It was then heated in glazed porcelain tubes to a bright heat, in vacua, for 
six hours. 

Sodium Thiosulphate. The sodium thiosulphate used was re-crystallised from 
water four times and was dried, in vacuo, over calcium chloride ; it was pure white in 
colour and its solution was neutral to litmus. 

Sodium Hydrogen Carbonate. The sodium hydrogen carbonate used for the 
preparation of carbonic acid, in an atmosphere of which the titration of the iodine 
contained in the combustion bulb was carried out, was purified by exposing the solid, 
at 70 C., to the action of a slow stream of carbonic acid gas passing through it. The 
carbonic acid was prepared by the action of hydrochloric acid on marble, and, before 
reaching the carbonate, was washed thoroughly with water. When the current of 
gas had been passing for three hours, the carbonate was allowed to cool in it until 
the ordinary temperature had been reached. Sodium hydrogen carbonate so prepared 
had no effect in impairing the accuracy of titrations of thiosulphate by means of the 
standard solution of iodine in potassium iodide. The gas obtained on heating the 
acid carbonate was completely absorbed by potassium hydrate. 

Starch Solution. The solution of starch, used as an indicator, was prepared by 
adding soluble starch, in very small quantities at a time, to boiling water which had 
been purified. When the solution commenced to assume a faint opalescent blue, the 
addition was discontinued. The solution, on cooling, was preserved in a tightly 
stoppered bottle, and to prevent any fermentation, a little mercuric iodide was added 
and dispersed through the solution by vigorous shaking. 

Platinised Pumice. Pumice stone was ground into small fragments and sifted 
through two sieves the first of 2 sq. millims. mesh, the second 1 sq. millim. ; the 
part remaining on the second was transferred to a porcelain basin and washed 
thoroughly with aqua regia. After decanting the supernatant acid, the mass was 
washed with water until the washings were no longer acid. It was then dried in a 
porcelain crucible contained in an air-bath at 120 C. The dried product was 
saturated with a concentrated solution of platinic chloride, excess of ammonium 
hydrate added, and the mass stirred until the yellow colour of the platinic chloride 
had disappeared from the supernatant liquid, which was then decanted and the 
platinised pumice carefully dried. It was then heated in a deep porcelain crucible 
until fumes were no longer evolved. A lid was placed on the crucible and the whole 
heated to a dull red heat for twelve hours. On cooling, the platinised pumice was 



ON THE ATOMIC WEIGHT OF CHLORINE. 185 

packed into the small U-tube B (fig. 1), which was then fused to the apparatus for 
the preparation of hydrogen. 

Purification of the Mercury used in the Pumps. The mercury was frequently 
cleaned as follows : It was placed in a suction flask, and on to its surface was poured 
a weak solution of nitric acid. The side tube of the flask was attached to the water 
pump, which drew air through the mercury by means of a glass tube held in position 
by a cork in the neck of the flask. 

This stream of air, coupled with the intimate mixing of the mercury and the nitric 
acid, resulted in the rapid oxidation and solution of all metallic impurities contained 
in the metal. When this had been accomplished, the mercury was thoroughly 
washed with water, dried with filter paper, and filtered, by means of very fine holes, 
through clean white paper. 

Cleaning of Glass Apparatus. Before use, all glass apparatus was filled with a 
hot mixture of potassium dichromate solution and concentrated sulphuric acid and 
allowed to stand for six hours. It was then washed out with boiling distilled water, 
and filled with hot concentrated nitric acid and allowed to stand overnight. The 
next morning the vessel was emptied, thoroughly washed out with hot distilled 
water, and steamed for three hours. Finally, a current of hot air, filtered through 
cotton-wool and dried through sulphuric acid, was passed through it until it was 
completely dried. 

6. Weighing the Bulbs, 

The balance, made specially for atomic weight determinations, was placed on a 
stone pedestal in a cellar, situated in the basement of the chemical laboratories. 
Observations with a maximum and minimum thermometer showed that the tempera- 
ture in this cellar varied but little. Three filter funnels filled with calcium chloride 
were kept inside the balance case ; the air in it was assumed to be half dried. The 
doors of the balance case were closed and half-an-hour allowed to elapse before a 
weighing was made. 

The vibrations of the pointer over the scale were viewed through a mirror by 
means of a telescope. Assuming the number of divisions on the scale to be 1000, and 
the average zero at no load 500, then the range of the zero variations, during our 
experiments, was 9 divisions, between 49G to 505. 

The sensibility of the balance, during the weighings of the chlorine bulb, was 
approximately 206 divisions for 1 milligramme, with a range of variation of 8 divisions. 
During the weighings of the hydrogen bulb, the sensibility was approximately 
198 divisions for 1 milligramme, with a range of variation ecpual to 10 divisions. The 
method of weighing adopted was GAUSS' method of reversals. Generally, five 
weighings were taken on one side and four on the other. The concordance of the 
individual weighings showed that their mean could be relied on to 4 divisions or 
00002 gramme. 

VOL. CCV. A. 2 B 



186 



PROFESSOR H. B. DIXON AND MR. E. C. EDGAR 



The weights employed were a brass hectogramme and its subdivisions to a gramme, 
and, for the submultiples of a gramme, small platinum weights. The hectogramme 
was taken as the unit and the separate weights were carefully compared with it. 
Since all our measurements of mass were relative and not absolute, it was not necessary 
to determine the absolute mass of our unit. In comparing the gramme of platinum 
with the brass gramme marked Z. a correction was applied for the different weights 
of air displaced by them. The values of all the weights are given below : 

VALUES of the Brass Weights. 



Nominal value. 


Value found. 


100 grammes (unit) 
50 


100-00000 grammes 
50-00005 


20 




19-99973 




10 


(A) 


10-00002 




10 


(B) 


9-99986 




5 




4-99991 




2 




1-99994 




1 


(I) 


1-00025 




1 




99998 




1 


(H) 


99993 





VALUES of the Platinum Weights. 



Nominal value. 


Value found. 


5 gramme 
2 


49998 gramme 
19994 


1 
1 
05 


(1) 

(2) 


09996 
09992 
04995 




02 




02001 




01 
01 
Ptri 


(1) 
:ler 


01001 
01000 
01007 





The palladium bulb, when charged with hydrogen and sealed off, varied in weight 
from about 419 grammes to 425 grammes. It was counterpoised by a vessel made of 
the same glass and of approximately the same volume, weighing 400 '00097 grammes. 
The brass and platinum standardised weights were used to complete the equilibrium. 
The only vacuum corrections necessary to apply to the weighings were (i.) that for 
the difference in volume between the small weights used before and after the com- 
bustion, i.e., the volume occupied by (approximately) 1 gramme of brass, and (ii.) for 
possible changes in the buoyancy of the bulb. 

The glass counterpoise was made the same volume as the bulb when first used in 
Experiment I. It was not considered necessary to alter it so as to make it exactly 



ON THE ATOMIC WEIGHT OF CHLOEINE. 



187 



the same volume as the bulb in the subsequent experiments, since the maximum 
variation in the displacement of the bulb did not exceed 1'3 cub. centim. This 
variation in volume, caused by differences in sealing off the thick-walled capillary 
tube, may be assumed to be due to the solid glass drop at the sealed end. When the 
density of the air altered between the first and second weighings of the bulb, a 
difference between the displacement of the bulb and the counterpoise might affect the 
apparent weight of the bulb, but in only one experiment (No. 8) was a correction 
necessary, and that only a unit in the fifth place of decimals. 

The weighings of the chlorine bulb were carried out in the same manner, with a 
similar glass counterpoise. It was not, of course, necessary to obtain the same degree 
of accuracy in weighing the chlorine as in weighing the hydrogen, since a unit in the 
fourth place of decimals is insignificant. Variations in the displacement of the 
chlorine bulb, caused by sealing-off, though considerably larger than those of the 
hydrogen bulb, did not affect the determination of the " chlorine taken." 

In illustration of the method of weighing we may refer to Experiment V. The 
palladium bulb (charged with hydrogen) required the following weights to be added 
to the opposite pan : 



Weights used. 



Value. 



Brass 20 grammes 

Ft '5 

02 

01 (1) 

01 (2) 

Pt rider on 2nd division 



19-99973 grammes 
49998 
02001 
01001 
01000 
00201 



20-54174 grammes 



Five weighings with the weights in the right-hand pan gave a mean zero of 
398 '2 divisions on the sale. Four weighings with the weights reversed gave a mean 
zero of 597. With no load the mean zero was 497. The two differences are : 

Eight 98-8. Left lOO'O. Mean 99'4. 

The sensibility under this load was found to be 202 divisions of the scale for a 
difference of 1 milligramme. The mean displacement of the zero was, therefore, equal 
to a weight '00049 gramme to be subtracted. 

Adding these weights together 

Counterpoise + 400 00097 grammes 
Weights + rider + 20-54174 
00049 



420-54222 



2 B 2 



188 PROFESSOR H. B. DIXON AND MR. E. C. EDGAR 

In this experiment the palladium bulb has a volume below that of the counterpoise 
by rather less than '5 cub. centim. The mean barometric pressure at the first 
weighing was 7G6'1 millims., and the mean temperature was 14'5 C. At the second 
weighing, after the combustion, the mean barometric pressure was 761'2 millims., and 
the tempei'ature was 12 0- 1 C. The difference in weight of - 5 cub. centim. of air 
measured under these conditions is only - 001 milligramme, and is therefore negligible. 

Subjoined are the details of the weighings of the palladium bulb in Experiment V 

EXPERIMENT V. Before Combustion. 

Temperature of balance (at start of weighing) 14 -5 C. 

(at end )14-GC. 

Barometric height (at start of weighing) 766' 7 millims. 

(at end 765-5 

Weights used were: 20, - 5, '02, -01 and -01. Rider on 2nd division on beam. 
Zero at no loud .... 498. 

,, (weights in right pan) 393. Mean zero at no load 497. 

,, ( ,, ,, left ,, ) 009. Zero (weights in right pan, mean of 5) 398 -2. 

( right ) 390. 

( ,, left ) 591. ( left 4) 597. 

at no load .... 49G. 

(weights in right pan) 404. Sensibility 202. 

( left ) 599. 

( right ) 408. 

( left ) 589. 

( right ) 396. 

at no load .... 498. 

Weight of bulb (before experiment) 420-54222 grammes. 

EXPERIMENT V. After Combustion. 

Temperature of balance (at start of weighing) 11 -8 C. 

(at end )12-4C. 

Barometric height (at start of weighing) 760-5 millims. 

(at end )761'9 

Weights used were: 10 (A), 5, 2, 1 (I), 1 (Z), -5, -02, -01 (1), and rider on 5th division. 
Zero at no load .... 503. 

(weights in right pan) 480. Mean zero at no load 501. 
.. ( left ) 514. 

( r ig nt ) 488. Zero (weights in right pan, mean of 5) 489 4. 
,, at no load .... 501. 

(weights in left pan) 513. ( left 4)512-8. 

,1 ( right ) 496. 

( .. left ) 509. Sensibility 201. 

( ., ,i right ) 492. 

( ,, ,, left ) 515. 

( right ) 491. 

,, at no load .... 499. 

Weight of bulb after experiment 419-53605 grammes. 



ON THE ATOMIC WEIGHT OF CHLORINE. 189 

7. Method of Carrying Chit the Combustion. 

The weighings of the palladium bulb and the chlorine condensation bulb completed, 
the next step was to set up the combustion apparatus (fig. 5). This consisted of a 
stout glass globe A, the " combustion globe " made of Jena glass. Its capacity was 
about 750 cub. centims., and it was provided with three ground-glass tubulures. In 
order to ignite the hydrogen at the jet, two platinum-iridium wires* (totally enclosed, 
save for their extreme tips, in glass covers) were fused into the combustion globe on 
each side of the hydrogen tubulure. By the passage of electric sparks between their 
tips, the jet of hydrogen was easily ignited. 

Into the combustion globe was run sufficient water to absorb all the hydrochloric 
acid gas formed during the combustion, and to leave dilute acid of a not greater 
strength than one-seventh concentrated. Then two very thin glass bulbs (capacity of 
each about 6 cub. centims.), which had been previously filled with a hot, concentrated 
solution of potassium iodide and sealed, were cautiously slid into this water through 
one of the tubulures. The palladium bulb B, the chlorine condensation bulb 0, and 
the three-way tap D were then, respectively, fitted to the tubulures E, F, and G, care 
being taken that none of the lubricant (phosphoric acid) was squeezed into the 
combustion globe through -the interstices of the ground-glass joints. To one limb of 
the three-way tap D, a generator of carbonic acid in an atmosphere of which the 
subsequent titration of residual iodine was carried out, was attached by a short length 
of thick-walled indiarubber tubing ; to the third limb was fused the apparatus H, 
through which any residual gases from the combustion were drawn. It consisted of a 
wash-bottle which could be taken to pieces by means of the ground-glass joint J. 
The tap K controlled the passage of the gases through the liquid, an alkaline solution 
of sodium thiosulphate, contained in the wash bottle. 

The tube L was attached to the mercury pump by a short piece of thick-walled 
indiarubber tubing. 

These two short lengths of indiarubber tubing were employed so as to enable us to 
give a jerking motion to the combustion globe and the bulbs when fitted together : 
(i.) to break the drawn-out cul-de-sac of the chlorine bulb, and (ii.) to break the 
potassium iodide bulbs after the combustion. The only danger arose from a possible 
in-leakage of air through the tube connecting the wash-bottle with the pump, by 
which the residual oxygen, nitrogen, and hydrogen were withdrawn from the globe. 
This tube was wired on to the glass when hot, and was well " drowned" before being 
used to evacuate the globe. We found that no readable volume of air had leaked 
through into the highest vacuum attainable during three days. 

The different parts of the combustion apparatus having been fitted together, the 
strength of a neutral solution of sodium thiosulphate was determined by titrating a 

* The position of these wires is shown by the dotted lines P and PI ; they lie in a plane at right angles 
to the vertical section shown in fig. 5. 



190 



PROFESSOR H. B. DIXON AND MR. E, C. EDGAR 




I 

I 
o 



60 



ON THE ATOMIC WEIGHT OF CHLORINE. 191 

measured volume against the standard solution of iodine in potassium iodide. A 
measured amount (about 6 to 7 cub. oentims.) of the sodium thiosulphate solution 
was run into the wash-bottle and made alkaline by the addition of sodium hydrogen 
carbonate. The taps D and K were now opened, and the combustion apparatus 
evacuated (in a stream of water-vapour) as far as possible by the pump. A rapid 
stream of water- vapour was produced by immersing a large condenser, fused to the 
pump, in a freezing mixture of ice and salt, and by gently warming the lower part of 
the combustion globe with warm water. This was done to facilitate the removal of 
traces of air and nitrogen, and that this was accomplished we concluded from the 
small amount of nitrogen discovered in the subsequent gas analysis. During the last 
period of the exhaustion, the calcium chloride and ice freezing mixture, in which the 
bulb containing liquid chlorine was immersed during the combustion, was prepared, 
placed in a wide-necked, unsilvered Dewar tube, and packed well round the liquid 
chlorine bulb. 

The evacuation completed, the taps D and H were closed, and the glass cul-de-sac M 
broken by jerking the glass rod N against it. 

The heating of the palladium bulb, enclosed in a stout copper box covered witli 
asbestos sheet, was next started, the temperature being noted by means of a mercury- 
nitrogen thermometer. 

The temperature of the liquid chlorine was now between 25 C. and 30 C., and 
the pressure on the special tap Q was therefore not greatly above atmospheric. 
Q was slightly turned so as to admit chlorine slowly into the combustion globe. 
When the pressure of gas in the globe had become nearly atmospheric, the tap Q was 
closed. This point was determined by the change in the faint hissing noise which 
attended the entry of chlorine into the vacuum. When the palladium bulb had 
reached a suitable temperature, all lights were turned out. 

Next came the ignition of the jet of hydrogen. Whilst a rapid succession of sparks 
was passed between the platinum-iridium tips, the tap N was very cautiously opened 
so as to admit the hydrogen slowly into the combustion globe. The moment the jet 
of hydrogen had ignited the sparks were discontinued, and all attention was centred 
on the flame. To cool the globe during the combustion, ice was packed round the 
lower portion, while that part which was immediately above the flame was cooled by 
a stream of cold water. 

To avoid, as far as possible, any diffusion of hydrogen through the flame, the 
combustion was carried out at a pressure only slightly below atmospheric. The 
atmosphere of chlorine was constantly replenished through the tap Q, whilst the 
tap N regulated the admission of hydrogen to the flame. 

The combustion of hydrogen in chlorine at a glass jet is an interesting phenomenon. 
The flame can be divided into two zones an inner zone of a light apple-green colour, 
with an outer zone of less pronounced hue. We learnt by experience that three 
points in connection with the flame were important for our purpose. Firstly, the 



!92 PEOFESSOE H. B. DIXON AND ME. E. C. EDGAE 

gradual elongation of the outer zone, together with a lessening of the luminosity ol 
the inner zone, indicated that the atmosphere of chlorine was riot being renewed 
quickly enough. Secondly, when the flame became smaller and more luminous, we 
knew that the pressure of chlorine was in excess, and that the gas was being admitted 
into the globe too quickly. Lastly, a gradual shrinking in the size of the flame, 
unattended by any change of luminosity, indicated that the supply of hydrogen was 
failing. This was, of course, remedied by raising the temperature of the palladium bulb. 

When the combustion had been carried to such a point that only a drop of liquid 
chlorine was left in the condensation bulb, the tap Q was finally closed and the flame 
made very small. As the atmosphere became rarefied, the outer zone of the flame 
became elongated and less luminous ; the inner zone changed also, but to a less extent. 
In one experiment (IV.), the flow of hydrogen not being reduced as the chlorine- 
atmosphere became rarefied, a flame passed through the whole globe. Just before 
the point of extinction the tap N was closed and the combustion was ended. The 
duration of the combustion was about three hours, during which constant watching 
was necessary. The palladium bulb was now allowed to cool to the ordinary 
temperature. 

The two small bulbs, containing concentrated solution of potassium iodide, were 
then 'broken by dashing them against the interior of the combustion globe, when the 
residual chlorine was absorbed with precipitation of iodine. The precipitated iodine, 
however, soon dissolved in the excess of potassium iodide. The tap D was opened 
and the residual gases were sucked out of the combustion globe in a current of water- 
vapour through the alkaline solution of sodium thiosulphate contained in the wash- 
bottle H, in which the vaporised iodine was absorbed. The residual gases were 
collected in the gas analysis apparatus. 

During this exhaustion the long glass tube R connected with the three-way tap D, 
and containing NaHCO :i , had been heated. The evacuation completed, D was turned 
and CO a admitted until the combustion globe was full. This was indicated by the 
escape of gas through the manometer. The tubulure G was now opened, cleaned 
from adhering phosphoric acid, and the residual iodine titrated in the atmosphere of 
carbonic acid by means of the sodium thiosulphate solution of known strength 
contained in a calibrated burette.* As sufficient potassium iodide was originally 
contained in the thin glass bulbs to dissolve easily the precipitated iodine, the titration 
was quickly and accurately carried out, five drops of starch solution being added 
towards the end of the titration. f One drop of the standard solution of iodine 
restored the blue starch-iodide colour to the decolourised liquid in the combustion 

h The two burettes employed were carefully calibrated by means of an Ostwald calibrator of 
2 cub. centims. volume. The mean results of two calibrations were tabulated and used in determining 
the volumes. 

t Owing to the action of hydrochloric acid on a solution of sodium thiosulphate, we were unable to add 
excess of the sodium thiosulphate solution and titrate back with the standard solution of iodine. 



ON THE ATOMIC WEIGHT OF CHLORINE. 



193 






B- 



Fig. G. Gas-analysis apparatus. 



globe, so it was evident that the error in our volumetric determinations of iodine 
must have been small. The alkaline sodium thiosulphate solution in the wash-bottle 
was exactly neutralised with very dilute hydrochloric acid, and the residual 
thiosulphate estimated with the standard iodine solution. 

The determination of the residual gases was effected as follows : Fig. 6 is a sketch 
of the gas-analysis apparatus employed.* It consisted of a graduated pipette A 
attached to a bent capillary tube, with stopcocks C and D and a graduated tube B. 
The weight of the apparatus, filled with mercury from ' 
the tap C to the end of the capillary tube E, having 
been determined, the whole was filled with mercury and 
placed in the trough. The gases, sucked out by the 
pump from the combustion globe, were collected in B 
and passed into A. It was assumed that the gases 
consisted of hydrogen, oxygen, and nitrogen. 

When the residual gases had been collected, the whole 
was transferred to the balance room and allowed to reach 
the temperature of the room. During this time the 
taps C and D (fig. 6) were, of course, left open ; they 
were then closed. In order to maintain the gases during 
analysis at not only constant temperature but constant 
pressure, it was necessary that the height of the mercury 
in the limb A of the gas-analysis apparatus above the 
surface of the mercury in the trough should be kept 
constant. With the aid of the two etched scales on 
A and B, the divisions of which were 1 millim. apart, this constant pressure could be 
easily attained by raising or depressing the apparatus in the trough until the mercury 
in the limb A stood the same height as before above the level of the mercury in 
the trough. 

When the gases had reached the temperature of the balance room, and the difference 
in level of the mercury in the limb A and of the mercury in the trough had been 
noted, the taps C and D were closed, B was emptied and the apparatus was then 
ready for weighing. The difference in the weights of the apparatus (i.) full of mercury, 
and (ii.) containing the residual gases of the combustion (corrected for the weight of 
these residual gases) gave, by an obvious process, their volume. 

After being weighed, the gas apparatus was transferred to the mercury trough, the 
platinum spiral F was then cautiously heated by an electric current so as to bring 
about the combination of all the hydrogen with the oxygen. Sometimes the oxidation 
was attended by an explosion ; this, of course, occurred when the percentage of 
hydrogen was relatively great. 

As can be seen from Table II., the oxygen was always in excess of that required 
* This form of gas-analysis apparatus was first used by D. L. CHAPMAN and E. HOPKINSON. 

VOL. CCV. A. 2 C 



194" PROFESSOR H. B. DIXON AND MR. E. 0. EDGAR 

for the complete combustion of the hydrogen. After B had been re-filled with 
mercury and the apparatus inverted in the trough, the taps C and D were opened, 
and consequent upon the contraction in volume of the gases, mercury rose in the two 
limbs A and B. When the whole had cooled to the temperature of the room, and 
the pressure had been equalised, C and D were closed and the apparatus again 
weighed as before. The difference between the second weighing and this last one 
gave the volume of contraction, i.e., gave the volumes of hydrogen and oxygen which 
had combined. 

The apparatus was again transferred to the mercury trough, C and D opened, and 
hydrogen admitted to the apparatus, sufficient to burn up the residual oxygen. The 
mercury levels were again adjusted, C and D were closed, and the apparatus again 
weighed. From weighings three and four the volume of the added gas was easily 
calculated. The gases were fired by heating the platinum spiral, and, on cooling, the 
apparatus was weighed as before. The final weighing, coupled with weighing four, 
gave the volume of contraction, i.e., gave the volume of residual oxygen. From the 
data thus obtained the composition of the residual gases of the combustion, assuming 
them to have been hydrogen, oxygen, and nitrogen, was easily calculated.* 

The analysis of the residual gases from Experiment 2 is given below in 
illustration : 

Mean temperature of balance room ............. 13-8C. 

,, barometric height ................. 768 '5 millims. 

Difference in level between mercury in limb A and mercury in trough . 198 '5 

Weight of gas apparatus full of mercury ........... 489-029 grammes. 

,, and residual gases .......... 413'756 

,, ,, ,, af tor combustion ........... 440 '846 

,, ,, addition of EL .......... 309-846 

combustion ........... 450-838 

From these weights the composition of the residual gases was calculated to be as follows : 

4-12 cub. centims. of oxygen ~\ ftt 13 . 8 c an(1 768 . 5 _ 198 . 5 millims . p ress ure. 
1'33 hydrogen > 

09 nitron-en I Gases saturated with aqueous vapour. 

These volumes gave, on reduction to N.T.P., 

2-87 cub. centims. of oxygen from steam-) at c alld 760 millimS- 

"93 ,, hydrogen S. 

08 air J Gases dry. 

Now, in accordance with the equation 



2-87 cub. centims. of oxygen were produced by the action on aqueous vapour of 5 -74 cub. centims. of 
chlorine. 

Weight of 5-74 cub. centims. of chlorine is 5-74 x -00317 = -0182 gramme. 

Weight of 93 cub. centim. of hydrogen = 00008 gramme. 

* In preliminary experiments, carried out in the same way, we failed to detect any trace of C0 2 in the 
products of combustion. 



ON THE ATOMIC WEIGHT OF CHLORINE. 195 

8. Results of the Experiments. 

In the following tables we have put together the results obtained in the nine 
experiments. Table II. contains the volumes of the several residual gases, reduced 
to normal temperature and pressure, as determined by the gas-analysis. 

We have assumed that the nitrogen found at the end of the experiments is due to 
residual air left in the evacuation of the large combustion globe. It is conceivable 
that a trace of this nitrogen came from the palladium bulb and was weighed as 
hydrogen. If that were so, the atomic weight of chlorine we have found would be too 
low. The total volume of nitrogen found in the nine experiments was '8 cub. centim. 
To make an extreme supposition if all this nitrogen had been introduced from the 
palladium bulb, and weighed as hydrogen, and therefore all the oxygen had come 
from the steam, the atomic weight of chlorine found by us would be '005 too low. 

In Table III. we have put together the several portions of residual chlorine not 
combining with the weighed hydrogen : (i.) that calculated from the iodine found in 
the globe ; (ii.) that calculated from the iodine vapour drawn over with the residual 
gases and caught in the wash-bottle; and (iii.) that calculated from the oxygen 
found in the residual gases less the oxygen assumed (from the nitrogen) to be present 
as air. 

In Table IV. the weights of the bulbs before and after the combustion are given, 
with the corrections for buoyancy and for the unburnt gases. We set out the 
hydrogen weighings to five places of decimals, although it is not, of course, suggested 
that the absolute weight of the palladium bulb can be determined to this degree of 
accuracy. The fifth figure does not affect the mean atomic weight deduced from the 
experiments. 



2 C 2 



196 



PKOFESSOR H. B. DIXON AND ME. E. C. EDGAR 



TABLE II. Determination of Volumes of Residual Gases, cub. centims. at N.T.P. 



Experiment 


I. 


II. 


III, 


IV. 


V. VI. 


VII. 


VIII. 


IX. 




















Volume of oxygen liberated from 










1 










3-39 


2-87 


5-07 


2-91 


4-30 3-41 


3-65 


3-11 


4-80 


Volume of hydrogen unburnt. . . 


1-51 


93 


2-02 


08 


40 -74 


1-04 


3-61 


2-45 


Volume of residual air 


11 


08 


06 


11 


1C -06 


18 


13 


12 



TABLE III. Determination of the Weight of Chlorine uncombined with the 
Weighed Hydrogen (in grammes). 



Experiment. 


I. 


II. 


III 


IV 


V 


VI 


VII 


VIII 


IX 






















Unburnt chlorine calculated from 
iodine in globe 


6941 


6603 


7865 


6238 


6767 


5981 


6838 


7999 


7260 


Unburnt chlorine calculated from 
iodine vapour 
Chlorine corresponding with oxygen 
liberated 


0005 
0215 


0006 

0182 


0004 
0321 


0003 
0185 


0007 
0273 


0005 
016 


0005 
0231 


0006 
0197 


0005 
0304 






















Total excess of chlorine . . 


7161 


6791 


8190 


6426 


7047 


6202 


7074 


7425 


7569 



ON THE ATOMIC WEIGHT OF CHLORINE. 



197 





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PROFESSOE H. B. DIXON AND MR. E. C. EDGAR 

APPENDIX. 

1. The Action of Chlorine on Glass. 

The following experiments were made to determine the action, if any, of pure, 
dry chlorine on soft glass. Two glass bulbs of approximately equal volume and 
weight were made. To one of these, A, was fused the inner portion of a ground 
glass joint ; it was then cleaned and dried. The two bulbs were then suspended from 
different pans of the balance and small weights added to one pan to bring them to 
equilibrium. A was then fitted to the apparatus for generating chlorine, and the 
whole was evacuated and filled with pure dry chlorine. The bulb was separated 
from the rest of the apparatus by fusion beyond the ground-glass joint and was then 
kept for one week. At the end of that time the ground-glass joint was taken to 
pieces, and the chlorine sucked out and replaced by dried air. It was then weighed, 
the other bulb acting as a counterpoise. 

Weight to counterpoise the bulb (before exposure to chlorine) . . 1 -32468 grammes. 
(after ) . . 1 32464 

The experiment was repeated with two similar bulbs, but the chlorine was left in 
contact with the glass for a fortnight. 

Weight to counterpoise the bulb (before exposure to chlorine) . . 2-67931 grammes. 

(after ) . . 2-67925 

Two more bulbs were subjected to similar treatment, the time of contact, in this 
case, being a month. 

Weight to counterpoise the bulb (before exposure to chlorine) . . 1 12884 grammes. 

(after ) . . 1-12879 

These weighings show that on allowing chlorine to remain in contact with soft 
glass for a considerable period of time, the latter loses weight very slightly. 

The bulb used in Experiment 1 was again filled with chlorine, which was allowed 
to remain in contact with the glass for a week. 

Weight of bulb before exposure 1 32464 grammes. 

after 1-32465 

An exposure for a further period of two weeks gave : 

Weight of bulb before exposure 1 32465 grammes. 

after 1-32463 

If any action of chlorine on the soft glass bulb may be assumed to have taken 
place, it must have occurred during the first week, as further exposure to chlorine 
gave a constant result. 



ON THE ATOMIC WEIGHT OF CHLORINE. 199 

The solvent action of liquid chlorine, if any, on soft glass was also examined. The 
same bulb was employed. After its weight had been determined as above, 10 cub. 
centims. of liquid chlorine were condensed in it by means of a freezing mixture of 
solid carbonic acid and ether. The bulb was then separated from the chlorine 
apparatus by fusion between the ground-glass joint and the bulb, and was laid aside 
for a week. The ground-glass portion was cleaned and dried, a mark was cut with a 
clean glass cutter in the glass capillary tubing attached to the bulb, and a clean 
fracture effected. When the chlorine in the bulb had been totally replaced by air, 
the three parts of the original apparatus, i.e., the bulb, the piece of glass broken off 
from it, and the inner portion of the ground-glass joint were weighed, the companion 
bulb acting as a counterpoise. 

Weight of bulb before exposure 1 32464 grammes. 

after 1-32466 

A similar apparatus was constructed, and, after being subjected to the action of 
pure dry gaseous chlorine for a week, the last experiment was repeated, the time of 
exposure being a month. 

Weight of bulb before exposure 3 49842 grammes. 

after 3-49839 

There seemed to be no appreciable action of liquid chlorine on soft glass. 

Though the combined effect of gaseous and liquid chlorine on soft glass was so 
exceedingly small, the bulb of the chlorine condensation bulb was subjected, before 
use, to the action of pure dry gaseous chlorine for a fortnight. 

2. The Reaction between Iodine and Sodium Thiosulphate in Presence of 
Carbonic Acid and of Hydrochloric Acid. 

Titrations of sodium thiosulphate by iodine in potassium iodide, carried out in an 
atmosphere of carbonic acid, showed that the gas had no influence on the accuracy of 
the residual iodine determinations. A known volume of sodium thiosulphate solution 
was run into a small Erlenmeyer flask and titrated with the standard solution of 
iodine in potassium iodide. An equal volume was run into another flask and pure 
carbonic acid (from sodium hydrogen carbonate) was passed through the solution for 
ten minutes, it was then titrated as usual. No difference in the volumes of iodine in 
potassium iodide solution required to combine with the thio in the two flasks could be 
detected. Several repetitions gave similar results. 

S. U. PICKERING* has shown that iodine in potassium iodide solution can be 
correctly titrated by thiosulphate in presence of hydrochloric acid, if allowance is 
made for the slow oxidation of the liberated hydrogen iodide by the oxygen from the 

* ' Jouru. Chem. Soc.,' 1880, p. 134. 



200 ON THE ATOMIC WEIGHT OF CHLOEINE. 

air. We have confirmed these experiments with different strengths of hydrochloric 
acid and found that practically no iodine was liberated in the oxygen free solutions 
employed. 

Approximately equal volumes of iodine in potassium iodide solution were run into 
small Erlenmeyer flasks X and Y from the calibrated burette B. The iodine in X 
was then titrated by means of thiosulphate solution from burette A ; hydrochloric 
acid of known strength was then added to Y and the titration immediately completed. 

The experiments were repeated several times with the addition of hydrochloric acid 
of j concentration : 

EXPERIMENT I. 

120 cub. centims. of -^ concentrated HC1 were added to the solution in flask Y. 

Volumes of iodine in K 1 taken. 
Burette B. Flask X, 25 04 cub. centims. Flask Y, 25 04 cub. centims. 

Volumes of thio required by above 
Burette A. Flask X, 25-13 cub. centims. Flask Y, 25 16 cub. centims. 

EXPERIMENT II. 

120 cub. centims. of i concentrated HG1 were added to the solution in flask Y. 

Volumes of iodine in K 1 taken. 
Burette B. Flask X, 25-08 cub. centims. Flask Y, 25-10 cub. centims. 

Volumes of thio required by above 
Burette A. Flask X, 25-21 cub. centims. Flask Y, 25-20 cub. centims. 

EXPERIMENT III. 

120 cub. centims. of i concentrated HC1 were added to the solution in flask Y. 

Volumes of iodine in K 1 taken. 
Burette B. Flask X, 25 23 cub. centims. Flask Y, 25 19 cub. centims. 

Volumes of thio required by above 
Burette A. Flask X, 25 31 cub. centims. Flask Y, 25 29 cub. centims. 

EXPERIMENT IV. 

120 cub. centims. of i concentrated HC1 were added to the solution in flask Y. 

Volumes of iodine in K 1 taken. 
Burette B. Flask X, 25-05 cub. centims. Flask Y, 25-06 cub. centims. 

Volumes of thio required by above 
Burette A. Flask X, 25-14 cub. centims. Flask Y, 25 1 7 cub. centims. 

Since hydrochloric acid of ^ concentration has then no influence on the titration of 
iodine in potassium iodide solution by sodium thiosulphate solution, we felt justified 
in using, in our experiments, such volumes of water as never permitted of the acid 
solution attaining a greater strength than j concentrated. 



[ 201 ] 



VI. Researches on Explosives. Part III. 

By Sir ANDREW NOBLE, Bart., K.C.B., F.R.S., F.R.A.S. 

Received June 8, Read June 8, 1905. 

[PLATES 1-13.] 

THE Researches which I venture to communicate to the Royal Society are, for the 
new explosives cordite, modified cordite, and nitro-cellulose, a continuation of the 
same modes of research, adopted in the experiments I made many years ago upon 
fired gunpowder with regard to the pressure and other phenomena attending its 
decomposition, and which appeared in the ' Philosophical Transactions.' * In the 
present investigations the same general methods have been followed, but with 
apparatus greatly improved and of much greater delicacy. 

The Academy of Sciences of France did Sir F. ABEL and myself the great honour 
to appoint MM. le General MORIN and BERTHELOT to report on our paper, and after 
giving an extended analysis of the results of our experiments the reporters con- 
cluded t : " Par cette analyse trop succincte de rimportant travail que MM. NOBLE 
et ABEL ont soumis au jugement de 1' Academic, on pent voir que malgre" certaines 
critiques auxquelles nul travail humain ne saurait echapper, 1'ensemble de leurs 
recherches n'en constitue pas moins une oeuvre capitale, propre a, jeter un grand 
jour sur toutes les questions qui se rattachent aux effets des poudres." 

A paper by M. BERTHELOT in the same No. of the ' Comptes Rendus ' draws 
attention to the chief point upon which that eminent chemist differed from ourselves. 

A study of the variations in the products when the decomposition of gunpowder 
was conducted under pressures widely different, varying in fact between 1 ton per 
sq. inch and 35 to 40 tons per sq. inch, led my lamented friend Sir F. ABEL and 
myself to state that, according to our view, "any attempt to express even in a 
complicated chemical equation the nature of the metamorphosis which a gunpowder 
of average composition may be considered to undergo, would only be calculated to 
convey an erroneous impression as to the simplicity or definite nature of the 
chemical results, and their uniformity under different conditions, while possessing no 
important bearing upon an elucidation of the theory of the explosion of gunpowder. " 

* NOBLE and ABEL, 'Fired Gunpowder,' Part I., 1875. 
t ' Comptes Rendus,' vol. 82, p. 492. 
VOL. CCV. A 392. 2 D 23.9.05 



202 SIE ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 

M. BERTHELOT, in the memoir to which I have referred, considers that the view 
which we took was contrary to all that was known in chemistry. 

It is no light thing to differ from so great an authority as M. BERTHELOT ; but the 
innumerable experiments I have since made with various modern explosives, in which 
the decomposition is of a simpler nature than that of fired gunpowder, have only 
confirmed me in the opinion that Sir F. ABEL and I then expressed. 

Thus in a paper published in the ' Proceedings of the Royal Society,'* I pointed 
out that when gun-cotton was fired under a great variation of pressure, the variations 
in the proportions of the resulting gases were both great and regular. In passing, 
for instance, from explosions under a pressure varying from 1'5 ton per sq. inch 
(2287 atmospheres) to 50 tons per sq. inch (76217 atmospheres) the volume of 
carbonic anhydride increased from 26'49 per cent, to 36'18 per cent., while the 
carbon monoxide decreased from 36'G6 per cent, to 27'57 per cent. 

There were also other differences, though not quite so marked, such as the steady 
decrease of free hydrogen and the large and steady increase of marsh gas. 

In the researches on gun-cotton to which I have alluded, certain data, such as the 
units of heat and the quantity of water formed by the explosion, although deter- 
mined, were not determined under the varying conditions with regard to pressure 
and the quantity and nature of the gases generated, under which the explosion 
took place. 

In the researches I am about to refer to, all the data connected with the explosion 
have been carefully determined, and I preface an account of the experiments 
themselves by a description of the varied apparatus adopted, or specially designed, 
for determining the tension of the gases generated by the explosion, the volume of 
the permanent gases and their nature, the quantity of water formed, the units ot 
heat generated, the time taken to complete the explosion under different pressures 
and different dimensions of the cords, tubes, or ribbons, these being the forms under 
which the explosives are generally made up. 

I have made experiments also to determine the time in which the exploded gases 
part with their heat to the walls of the vessel in which they are confined. 

These investigations have opened out many suggestive points, but in the present 
paper I propose to confine myself to a description of the apparatus used and the 
results obtained, giving also a resume of the calculations made to test the accuracy 
of the observations. 

Commencing with the apparatus for firing the explosives experimented with at 
different densities, obtaining the gases for analysis, and measuring their total volume, 
the vessel A., in Plate 1, is one of the explosion .cylinders used for these experiments ; 
B is the plug closing the vessel, on which also is shown the arrangement by which, 
when desired, the gas is allowed to pass at a small pressure through the tubes, either 

* ' Roy. Soc. Proc.,' vol. 56, p. 209. 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 203 

to the gasometer C or at pleasure into the gas tubes D, which, before the experi- 
ment, are filled with mercury, the stop-cocks above and below being closed ; E is 
a thermometer for determining the temperature of the gas when its volume is 
measured. 

Immediately after the explosion, if the vessel be quite tight, the valve at B is 
very slightly opened and the gas allowed to pass slowly through the tube F, containing 
pumice-stone and concentrated sulphuric acid, into the gasometer. 

When it is quite certain that all air is removed from the conducting tubes, the 
gas is allowed to flow into one of the gas tubes D, and shortly afterwards or at fixed 
intervals of time into the other two tubes, the quantity of gas in the tubes being 
added to that measured in the gasometer, the height of the barometer and the 
temperature of the gas at the moment of measurement being also determined. 

When the whole of the gas has been transferred to the gasometer, and the 
temperature and barometric pressure taken, the cylinder is opened. A considerable 
quantity of water is always found ; as much as possible of this water is collected by 
means of a weighed sponge placed in a weighed vessel, and closed by a ground glass 
plate. The amount of the water so collected is determined by weighing in the usual 
manner. 

After all the water that it is possible to remove with the sponge is collected, a 
weighed vessel of calcium chloride is placed in the cylinder, which is then closed, and 
left for one or two days, when the same procedure is followed with a second calcium 
chloride vessel, after which the cylinder is generally found to be perfectly dry. 

The next point to be determined is the amount of heat generated by the explosion. 

For this purpose a strong steel vessel, the section of which is shown in Plate 2, 
and of which the heat capacity is carefully determined, is employed. The calori- 
meter used is practically of the same construction as that described by OSTWALD in 
his ' Manual of Physico-Chemical Measurements.' 

A section of this calorimeter is also shown in Plate 2, the corresponding inner and 
outer surfaces of the several vessels being nickel plated. For some hours before the 
experiment the calorimeter is kept in a room maintained at as even a temperature as 
possible, the explosion vessel itself with the charge to be exploded being kept in the 
water as shown, so that the whole system may assume practically the same 
temperature. 

The rise of temperature due to the explosion being approximately known from 
previous experiments, the water in the outer cylinder before firing is kept at a 
temperature about half way between the initial and final temperatures of the inner 
vessel. 

The thermometers employed for these determinations are calorimetric, specially 
made for calorimetric experiments, and are only used for observing changes of 
temperature, and not for determining absolute values. The range of measurement 
in the thermometers I used was about 8 C., but by a special contrivance these 8 

2 D 2 



204 SIE ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 

can be brought to any point of the thermometric scale that may be desired. The 
temperature can be read approximately to O'OOl C. 

Full illustrations of a few of the calorimetric observations will be given with the 
corresponding calculations, and a resume of the results of the experiments at the end 
of the paper. 

The analysis of the gaseous products of explosion was carried out by means of 
SODEAU'S gas analysis apparatus,* the principal features of which are shown in 
Plate 3. 

Mr. SODEAU'S apparatus is admitted to be the most convenient that has been yet 
devised. I am indebted to him for the description of his apparatus and the mode of 
analysis followed. 

The tubes used for measuring and correcting for variations of temperature and 
pressure are placed in a cylindrical water-jacket. The measuring tube M is of 
50 cub. centims. capacity, and is graduated in -^-cub. centirn. divisions. Its upper 
end terminates in a capillary three-way stop-cock N, arranged so that the capillary K 
may be placed in communication either with the interior of the measuring tube or 
with the bent tube U containing water. The zero point of the graduation is at the 
outer side of the plug of the stop-cock N. The level tube L communicates with the 
measuring tube by means of a side branch, bent so as to prevent any entangled air 
bubbles from reaching the measuring tube. The lower end of the level tube is 
connected to a T piece, one end of which is provided with a stop-cock and leads to 
the mercury reservoir, whilst the other is prolonged across the table to a point near 
the reading telescope, where it terminates in a piece of thick-walled rubber tubing, 
the compression of which by a broad screw clip affords a means of accurately adjust- 
ing the level of the mercury without taking one's eye from the reading telescope. 

In order to render the apparatus more compact, the reading telescope is placed on 
the gas analysis table instead of on a separate support, and all graduations are 
consequently on the side opposite to that from which the stop-cocks are manipulated. 
An illuminating arrangement slides on the rod P. 

The corrections for variations of temperature and pressure are found by means of 
the "Kew Principle" correction tube C, which is so called because, as in the " Kew " 
barometer, the disturbance of the level of the liquid is allowed for in the graduation 
of the instrument, instead of being adjusted before each reading is taken. It 
consists of a cylindrical bulb having a stop-cock at its upper end, and attached below 
to a U tube, which is graduated on one limb and filled with water up to the zero 
mark whilst the stop-cock is open. The volume of air contained in the bulb is such 
that the water is displaced to the extent of one small division by a change of 
temperature and atmospheric pressure, which will cause a gas to experience an 
alteration of volume amounting to O'l per cent. These small divisions are further 

* 'Journal of the Society of Chemical Industry,' Feb. 28, 1903, page 187. 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 205 

subdivided into tenths by eye estimation. Errors of parallax are avoided by the use 
of a mounted lens sliding on the rod E, and the corrections are thus read directly in 
percentages as easily as the temperatures would be read by means of a thermometer. 

Absorptions are carried out in separate pipettes, one of which is shown in position. 
About 20 cub. centims. of the absorbent is usually confined over mercury in the 
bulb E, which is slightly inclined in order to facilitate the return of the unabsorbed 
gas. The horizontal bulb D receives the mercury displaced by the gas. The bulb F 
contains clean mercury, and, like the bulb E, can be placed in communication with 
the capillary G by means of the three-way stop-cock H. 

The explosion pipette resembles that of DITTMAR, but has a three-way stop-cock 
and mercury bulb arranged as in the absorption pipettes. 

In conducting an analysis, the sample tube is connected to the measuring tube by 
means of a capillary tube previously filled with mercury, and the gas drawn in by 
lowering the reservoir. After the mercury has been roughly levelled, the stop- 
cock N is turned so as to connect the capillary K with the tube U, and an absorption 
pipette, containing caustic potash solution, connected to the measuring tube by 
means of thick- walled rubber tubing, the ends of the capillaries being made to meet. 
A little water is then sucked through the capillaries into the bulb F, and mercury 
allowed to run back and fill the capillaries. The stop-cock leading to the large 
mercury reservoir having been closed, and the level tube being open to the atmo- 
sphere, the mercury is accurately levelled, as already described, and the volume ol 
the gas read by means of the reading telescope. A reading of the correction tube is 
also taken. 

In order to determine the amount of carbon dioxide present, the gas is driven over 
into the absorption pipette, followed by sufficient mercury to clear the capillaries, and 
the pipette well shaken in order to make the absorption complete. A little more 
mercury is then run over in order to clear away the potash from the bottom of the 
capillary attached to the absorption bulb, and the stop-cock N reversed so that the 
mercury in the capillaries runs into the tube U. The stop-cock N is then again 
turned and the gas slowly passes into the measuring tube, the rate being controlled 
by the stop-cock H, which is reversed as soon as the absorbent reaches it, so that the 
gas may be swept out of the capillaries by means of clean mercury from the bulb F. 
The stop-cock N is closed as soon as it is reached by the mercury. The gas is again 
carefully measured and the decrease of volume (after the correction for alteration of 
temperature and pressure has been applied) is equal to the amount of carbon dioxide 
originally present. The residue is then treated with alkaline pyrogallol, in order to 
ascertain whether any trace of air has been left in the connecting tubes during the 
collection of the sample and has so contaminated the gas. (This is more likely to 
occur when the explosion has taken place under feeble pressures and but little gas 
been produced.) If any oxygen is absorbed by the pyrogallol, its volume is multiplied 
by 4 '8 and the product (representing the volume of air present) deducted from the 



206 SIR ANDEEW NOBLE: RESEARCHES ON EXPLOSIVES. 

volume of gas taken for analysis, in order to obtain the volume of uncontaminated 
gas in the sample, and hence the correct percentages of the various constituents. 

Carbon monoxide is next removed by prolonged treatment with two successive 
portions of acid cuprous chloride solution. After absorption in the first cuprous 
chloride pipette the gas is directly transferred to a second pipette containing a 
solution which has not previously absorbed more than a trace of carbon monoxide, 
this transference being accomplished in practically the same manner as the return of 
the gas to the measuring tube, which takes place after transference to a pipette 
containing a little water, which removes the traces of hydrochloric acid derived from 
the cuprous chloride solution. An excess of oxygen* is then added, and, after 
measuring, the mixture is transferred to the explosion pipette, where it is exploded 
by means of an electric spark after expanding to such a volume as to prevent any 
marked oxidation of the nitrogen, whilst ensuring the complete combustion of the 
methane and hydrogen. The residue is next measured in order to ascertain the 
reduction of volume resulting from the explosion, and the carbon dioxide, produced 
by the combustion of the methane, is determined by absorption with potash. The 
volume of the carbon dioxide produced is equal to that of the methane originally 
present. The contraction due to the combustion of the methane, or in other words, 
twice the volume of the carbon dioxide, is deducted from the total contraction 
resulting from the explosion, and two-thirds of the corrected contraction so obtained 
is equal to the volume of hydrogen. 

Finally, the excess of oxygen remaining after explosion is determined by means of 
alkaline pyrogallol as a check upon the amounts of hydrogen and methane calculated 
as above. The nitrogen is estimated by difference. 

The above represents the routine determination of carbon dioxide, carbon monoxide, 
hydrogen, methane and nitrogen, as usually carried out, but additional tests have 
also been employed in order to ascertain whether certain other bodies were present in 
measurable quantities, but with negative results. Thus some of the gas samples 
were examined for unsaturated hydro-carbons (ethylene, &c.) immediately after the 
removal of the carbon dioxide, by shaking the gas with fuming sulphuric acid,t and 
removing acid fumes in the potash pipette before again measuring. No change of 
volume was ordinarily observed, and in no case did the change exceed O'l per cent., hence 
the samples did not contain any appreciable quantity of unsaturated hydrocarbons. 

The ordinary determinations of contraction resulting from explosion, carbon dioxide 

* The oxygen is prepared by the electrolysis of dilute sulphuric acid in a Hof mann voltameter and freed 
from traces of hydrogen by treatment in a Winkler combustion pipette. A supply is stored over mercury 
in one of the ordinary absorption pipettes ready for use. 

t Fuming sulphuric acid was used in one of the ordinary absorption pipettes, provided with a guard 
tube containing sulphuric acid, in order to prevent moisture from gaining access to the upper bulb D. 
Of course no mercury was employed in the absorption bulb, and that in the capillaries was driven into the 
bulb F when sending the gas into the pipette. 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 207 

produced, and oxygen consumed, do not afford a means of distinguishing methane 
from its homologues in presence of an excess of hydrogen ; thus ethane, together with 
its own volume of hydrogen, would give the same numerical results as two volumes 
of methane. A process of fractional combustion was therefore applied to some of the 
samples obtained from high density charges, as these contained large proportions ot 
saturated hydrocarbons. After removing carbon dioxide, carbon monoxide and 
unsaturated hydrocarbons, an excess of oxygen was added and the hydrogen was 
removed by repeatedly passing over gently heated palladinized asbestos contained in 
a capillary tube attached to a pipette containing water, as in the ordinary Orsat- 
Lunge apparatus, until no further decrease of volume occurred. The residual 
mixture was then examined by explosion, &c., in the usual manner. In each case the 
volume of carbon dioxide produced almost exactly half that of the decrease, 
resulting from the explosion, which latter was equal to the volume of oxygen 
consumed. These ratios agree with those required by the equation 

CH 4 +2O i = CO,+2H,0, 

but differ markedly from those which would result with the homologues of methane, 
thus even with ethane the proportions are 4:5:7 instead of 1 : 2 : 2. It therefore 
follows that the saturated hydrocarbons should be calculated as methane, none of the 
other members of the series being present in appreciable quantities. Examination 
of the water condensed in the closed vessel showed that the gas could not contain 
either ammonia or cyanogen in marked quantities, as the distribution under high 
pressure would so greatly favour the water. The presence of oxides of nitrogen is, 
of course, incompatible with that of a large proportion of hydrogen, as the gases 
have slowly cooled from a very high temperature. A trace of sulphuretted hydrogen, 
sufficient to markedly discolour mercury, exists in the gas when black powder is 
used as a lighter, but for all practical purposes the gaseous products of explosion 
may be regarded as consisting entirely of carbon dioxide, carbon monoxide, hydrogen, 
methane and nitrogen. 

One other arrangement of apparatus remains to be described, and that apparatus 
is used both for determining the time that explosives of various forms and natures 
require for their transformation, and for determining the rate at which they 
communicate the heat accompanying the explosion to the walls of the vessel in which 
the explosion takes place. 

The apparatus (see Plate 4) consists of an explosion vessel of the usual form, the 
explosion vessel being closed at its two ends by gas-tight plugs, through one of 
which pass the firing wires, while to the plug at the other end is fitted a pressure 
indicator. 

The pressure indicator is provided with a steel plunger of small area, which is 
exposed to the gas pressure. 

An enlarged continuation of this plunger engages the end of a spiral spring a, the 



208 SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 

resistance of which has been carefully determined. Attached to this plunger at I is 
a lever, the fulcrum of which, c, is fixed to the stationary bracket of the indicator, so 
that, when the spring is compressed, motion is given to the ends of the lever. 

Fixed to the lever are two electric magnets d, the one to record seconds, the other 
to perfect the firing circuit. A rocking bar e is coupled up over the seconds magnet, 
which is again coupled at the other end by a link /, thus conveying the seconds 
beats of the chronometer to the pen tracing its path on the revolving drum. 

The revolving drum itself is of light wood ; fixed to the frame are two rods gg, 
upon which slides the carriage for carrying the recording pen. The pen is held up 
by a detent, which is liberated by the firing current passing through the electro- 
magnet to which the detent is attached. There are two speeds given to the drum, 
the first a high speed (about 40 inches per second), the second very slow, about one 
inch per second. The drum is revolved by means of cord bands, which lead from the 
speed gear of the motor. 

Before firing, the fast-speed cord is made to drive the drum, the slow-speed cord 
running free ; about one or two seconds after the explosion the change speed 
lever is raised, thereby releasing the fast cord and tightening the slow cord. The 
fast speed is obtained approximately by watching the tachometer, but the actual 
speed is determined by measuring the length of the second on the recording 
diagram. The diagram is traced on a sheet of tin foil backed by paper. This is 
placed on the drum as shown on Plate 4, the edges being joined with gum, the 
surface being smoked black by camphor. 

The chronometer is of the ordinary marine type, but is furnished with a seconds 
make-and-break arrangement ; this being coupled up through a relay to the pressure 
lever, causes the recording pen to beat seconds till the desired curve is complete. 

The action of the apparatus during an experiment is as follows : 

All connections being made, the chronometer is coupled up, the pen carriage beating 
seconds, but no mark is yet made on the recording tin foil, the pen being held by the 
detent. The drum is started, and when it has reached the desired speed, as shown by 
the tachometer, the button of the firing battery is pressed and the circuit is completed 
at the beat of the next second. 

The current simultaneously releases the pen and fires the charge. As quickly as 
possible the speed is reduced by raising the speed lever and at the same time 
reducing the speed of the motor. The chronometer continues to beat seconds, thereby 
giving the relation between time and pressure until the experiment is concluded. 
The diagram is then removed from the drum by cutting through the point where the 
pen dropped, this being the beat of the second firing the charge. The sheet is then 
laid on a tray face up, flooded with thin varnish, and hung up to dry. 

For the purposes of these reseaches, which are specially directed to ascertain the 
differences in the phenomena attending the transformation of explosives fired under 
diiferent pressures, I have employed three explosives, viz., the cordite known as 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



209 



Mark I (for which the country has been indebted to the labours of Sir F. ABEL and 
Sir J. DEWAR), the modified cordite known as M.D., and a tubular nitrocellulose 
known as R. R. Rottweil. 

The general results, which I need not say have necessitated much calculation, are 
given in tables, but I think it necessary to give the results of a few experiments 
worked out in full, these being a fair sample of the whole series. In each case I give 
the reconciliation between the elements determined in the explosive and the same 
elements found in the gases after explosion. 

Taking into account the fact that the explosives themselves are not always of 
precisely the same composition, and also the nature of the experiments, the recon- 
ciliation to which I have referred is a very great deal closer than I expected. 

It has been suggested to me more than once that the mixture of the gases might 
not be homogeneous, that is, that tubes taken at different times from the explosion 
vessel might not give the same analysis. I have not found this to be the case. Thus, 
in an experiment where a charge of Rottweil R. R. was fired under a pressure of 
20'5 tons per sq. inch (3125 atmospheres), and a tube of the resultant gases was 
taken so soon as it was certain that all the air contained in the conducting tubes, &c., 
was displaced, a second tube being taken 6 or 7 minutes later, the analysis gave for 
the two tubes of permanent gases the following percentages : 



1st tube. 



2nd tube. 



C0 2 

CO 

H 

CH 4 

N 



28 '06 percentage volumes. 
34-02 
17-16 
7-41 
13-35 



28-02 percentage volumes. 
33-92 
17-00 
7-40 
13-66 



Taking now the data given by the explosion of a charge of 3 2 '6 8 grammes of M.D., 
which was fired at a density of O'l under a pressure of G - 9 tons per sq. inch 
(1051 '8 atmospheres), the resultant quantity of gas was 

27,486 cub. centims. at 16 0- 6 C., and under bar. pressure of 75T33 millims. 
= 25,916 cub. centims. at C. and 751 "33 millims. 
= 25,621 cub. centims. at C. and 760 millims. 

The quantity of water collected was 4136 grammes, equivalent to 5145'! cub. 
centims. aqueous vapour at C. and 760 millims. 

The percentage results of the analysis of the permanent gases in volumes are 
given in Column I., the total volumes in Column II, the percentage volumes, 
including aqueous vapour, are shown in Column III., and the percentage weights of 
the total gases in Column IV. 

VOL. ccv. A. 2 E 



210 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 





I. 


II. 


III. 


IV. 




Percentage 
volumes, 


Total, 
permanent gases, 


Percentage 
volumes, total 


Percentage 
weights, total 




permanent gases. 


cub. centims. 


gases. 


gases. 


C0 2 . 


20-10 


5,149-8 


16-74 


30-82 


CO .... 


40-70 


10,427-7 


33-90 


39-71 


H . . . . 


23-10 


5,918-4 


19-24 


1-61 


CH 4 . . . 


1-00 


256-3 


0-83 


0-55 


N . . . . 


15-10 


3,868-8 


12-57 


14-74 


H 2 ... 








16-72 


12-57 



The reconciliation between the amounts of C, O, H and N, contained originally in 
the explosive, and found in the products of explosion, were obtained as follows : 





C,. 


2 . 


H 2 . 


N 2 . 


CO.,* 
CO ... 
H . . . 

CH 4 * . . 

N . . . 


0-2010 
0-4070 
0-2310 

o-oioo 

0-1510 


0-1005 
0-2035 

0-0050 


0-2010 
0-2035 


0-2310 
0-0200 


0-1510 


Total 


s . . . . 


0-3090 


0-4045 


0-2510 


0-1510 





Multiplying the carbon, oxygen, and nitrogen by 12, 16, and 14 respectively, we 
obtain : - 





C 2 . 
grammes. 

3-708 


0,. 

grammes. 
' 6-472 


H 2 . 
grammes. 
0-2510 


N 2 . 
grammes. 
2-114 


And again multiplying by 2 295 


25,621-0 , 






11,160-7 


Add the H 2 

In M.D. cordite 
Difference 


C 2 . 
grammes. 
8-510 


2 . 
grammes. 
14-85 
3-67 


H 2 . 

grammes. 
0-57 
0-46 


N 2 . 
grammes. 
4-850 


8-51 
9-11 


18-53 
18-66 


1-03 
1-030 


4-85 
4-49t 


-0-60 


- 0-13 


o-oo 


+ 0-36 



In this experiment the quantity of gas and water measured shows that 1 gramme 
of M.D. under the pressure named above gave rise to 788 '4 cub. centims. of 
permanent gases, or to 946 '4 cub. centims. including aqueous vapour. 

@ A 



* Using HOFMANN'S notation : 
t Including N in cylinder. 





SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



211 



Again, with a charge of 99 '65 grammes of M.D. cordite and a density of 0'3, the 
gaseous pressure being 27'62 tons per sq. inch (4210'3 atmospheres), the quantity 
of gas measured, after being reduced to C. and 760 millims. pressure, was 
72,768 cub. centims., while the quantity of water collected was 11 '162 grammes, 
equals 13,885'5 cub. centims. aqueous vapour at C. and 760 millims. pressure. 





I. 


II. 


III. 


IV. 


Percentage 
volumes, 
permanent gases. 


Total, 
permanent gases, 
cub. centims. 


Percentage 
volumes, 

total gases. 


Percentage 

weights, total 
gases. 


CO, . . . 
CO ... 
H . . . . 
CH 4 . . . 
N . . . . 
H 2 . . . 


29-40 
31-10 
17-75 
6-55 
15-20 


21,393-7 
22,630-9 
12,916-4 
4,766-3 
11,060-7 


24-69 
26-12 
14-91 
5-50 
12-76 
16-02 


42-07 
28-32 
1-16 
3-41 
13-91 
11-13 



From the above data it appears that the explosion gave rise to 735 cub. centims. 
of permanent gas and 87 5 '3 cub. centims. total gas when reduced to C. and 
760 millims. pressure. 

RECONCILIATION. 





C 2 . 


2 . 


H,. 


N 2 . 


CO,. . . 0-294 
CO ... 0-311 
H . . . ; 0-1775 
CH 4 . . . 0-0655 
N . . . 0-152 


0-147 
0-1555 

0-03275 


0-294 
0-1555 


0-1775 
0-1310 


0-152 


1-000 0-3352 0-4495 0-3085 0-152 


x!2 x!6 xl4 


= 4-022 7-192 0-3085 2-128 



72 768'0 
Multiplying again by = 6 '520, we have as the weights found in grammes : 



Adding for H 2 

Totals 
In cordite before explosion 

Difference 



C 2 . 
26-22 


2 . 

46-89 
9-92 


H 2 . 
2-01 
1-24 


N 2 . 
13-88 


26-22 
27-05 


56-81 
56-26 


3-25 
3-33 


13-88 
13-36 


-0-83 


+ 0-55 

2 E 2 


-0-08 


+ 0-52 



212 



SIR ANDREW NOBLE: EESEARCHES ON EXPLOSIVES. 



Again, taking from Experiment 1416 an example of transformation at a high 
pressure, a charge of 81 grammes (including lighter) of Mark I cordite fired under a 
pressure of 22'5 tons per sq. inch (3429'8 atmospheres), the quantity of gas generated 
after being reduced to C. and 760 millims. pressure was 54, 961 '5 cub. centims. 
As before, the percentage in volumes of the permanent gases is shown in Column L, 
of the total gas in Column III., and the respective weights of the total gases in 
Column IV. 

The quantity of H 2 O collected was 11 '96 grammes = 14,878'2 cub. centims. aqueous 
vapour at C. and 760 millims. 





I. 


II. 


III. 


IV. 




Percentage 
volumes, 


Total, 
permanent gases. 


Percentage 
volumes, total 


Percentage 
weights, total 




permanent gases. 


cub. centims. 


gases. 


gases. 


CO, . . . 


31-30 


17,203-0 


24-63 


41-95 


'CO ... 


29-50 


16,213-7 


23-22 


25-15 


H . . . . 


18-50 


10,167-8 


14-56 


1-13 


CH 4 . . . 


1-95 


1,071-7 


1-53 


0-95 


N . . . . 


18-75 


10,305-3 


14-76 


16-02 


H,0 . . . 








21-30 


14-80 



These data give the quantity of permanent gases generated at 686 "4 cub. centims. 
and the total gases at 869 - 7 cub. centims. per gramme. 

Proceeding to compare as before the elements in the cordite and in the exploded 
gases, we have : 





C* 


2 . 


H 2 . 


N 2 . 


C0 2 . . . 
CO ... 
H . . . 
CH 4 . . . 

N . . . 


0-3130 
0-2950 
0-1850 
0-0195 

0-1875 


0-1565 
0-1475 

0-0098 


0-3130 
0-1475 


0-1850 
0-0390 


0-1875 


0-3138 0-4605 0-224 0-1875 


x!2 x 16 x!4 


=3-766 7-368 0-224 2-625 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



213 





' 11,1607 




we nave lur > 


veigrits in 


Add for H 2 

Totals 
The cordite 


C 2 . 
18-55 


2 . 
36-28 
10-63 


H 2 . 

1-10 
1-33 


N 2 . 
12-93 


18-55 
18-47 


46-91 
46-94 


2-43 
2-43 


12-93 
12-46 



Difference 



+ 0-08 



-0-03 



0-00 



+ 0-47 



Experiment 1401. At a density of 0'4 a charge of 128'5 grammes of Rottweil 
nitrocellulose E.R., giving a pressure of 34 - 9 tons per sq. inch (5320'0 atmospheres), 
generated 88,689 cub. centims. at C. and 760 millims. pressure, also 15 '2 3 grammes 
of water = 18,946'! cub. centim. of aqueous vapour at C. and 760 millims. 

GAS ANALYSIS. 





I. 


II. 


III. 


IV. 




Percentage 


Total, 


Percentage 


Purcenta 




volumes, 


permanent gases, 


volumes, total 


weights, tc 




permanent gases. 


cub. centims. 


gases. 


gases. 


C0 2 . . . . 


33-70 


29,888-2 


27-44 


45-80 


CO .... 


28-90 


25,631-1 


23-53 


24-99 


H . . . . 


14-20 


12,593-8 


11-56 


0-88 


CH 4 ... 


9-85 


8,735-9 


8-02 


4-87 


N . . . . 


13-35 


11,840-0 


10-87 


11-57 


H 2 . . . 








18-58 


11-89 



Hence we have 690 '1 cub. centims. of permanent gases, or 8 46 "8 cub. centims. 
including aqueous vapour per gramme of explosive. Proceeding to reconcile the 
elements, we have : 





C 2 . 


2 . 


H a . 


N 2 . 


C0 2 . . . 
CO ... 
H . . . 
CH 4 . . . 

N . . . 


0-3370 
0-2890 
0-1420 
0-0985 
0-1335 


0-1680 
0-1450 

0-0495 


0-3370 
0-1340 


0-1420 
0-1970 


0-1335 


1-0000 0-3625 0-4810 0-3390 0-1335 


x!2 x!6 x!4 


= 4-350 7-700 0-339 1'870 



214 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



Multiplying again by 



Add H 2 

Totals 
In the R.R. nitrocellulose 

Difference 



= 7'947, we have the weights :- 



C 2 . 


2 . 


H 2 . 


N 


grammes. 


grammes. 


grammes. 


grammes. 


34-57 


61-08 


2-69 


14-83 





13-54 


1-69 





34-57 


74-62 


4-38 


14-83 


35-85 


73-33 


4-06 


15-16 



-1-28 



+ 1-29 



+ 0-32 



-0-33 



In the reduction of the experiments hitherto considered, it has not been necessary 
to make any correction to the quantity of gas, as the weight of the gases sufficiently 
accurately represents the weight of the explosive experimented on, but it occasionally 
happens, especially at high pressures, that, at the moment of firing, a puff of gas 
escapes, the leak, however, being generally only momentary, the explosion vessel 
becoming later perfectly tight. In these cases of course the weight would be in 
defect, but in a few cases the weight of the gases was in excess, and I proceed to 
show how these experiments were dealt with. 

Experiment 1417. At a density of 0'45 a charge of 143'91 grammes of M.D. 
cordite, giving a pressure of 43'22 tons per square inch (6588'2 atmospheres), 
generated 98,231-9 cub. centims. at C. and 760 millims. pressure; the water 
collected was 15'59 grammes = 19,384'0 cub. centims. The analysis of the perma- 
nent gases in volumes gave : 





I. 


II. 


III. 


IV. 


Percentage 
volumes, 
permanent gases. 


Total, permanent gases. 


Percentage 
volumes, total 
gases. 


Percentage 
weights, total 
gases. 


C0 2 . . 

CO .... 
H . . . . 

CH, . . . 

N . . . . 
H.O . . . 


36-6 
24-8 
11-9 
10-7 
16-0 


cub. centims. grammes. 

35,952-9 = 70-86 
24',361-5 = 30-55 
11,689-6 = 1-05 
10,510-8 = 7-54 
15,717-1 = 19-76 


30-56 
20-71 
9-94 
8-94 
13-36 
16-49 


48-75 
21-02 
0-72 
5-19 
13-59 
10-73 



Now if to the weights given in Column III. we add the weights of water, it will 
be found that the total weight is 1'44 grammes greater than the charge actually 
employed. The volume of the gases has therefore been reduced to 97,589'5 cub. 
centims., thus giving 676'3 cub. centims. of permanent gases or 810'6 cub. centims. 
total gas for each gramme exploded. 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 
RECONCILIATION. 



215 





C 2 . 


2 . 


H 2 . 


N 2 . 


C0 2 . . . 
CO ... 
H . . . 
CH 4 . . 

N . . . 


0-366 
0-248 
0-119 
0-107 
0-160 


0-183 
0-124 

0-054 


0-366 
0-124 


0-119 
0-214 


0-160 


1-000 0-361 0-490 0-333 0-160 


x!2 x!6 x!4 


= 4-332 7-840 0-333 2-240 



Multiplying again by 



Add H 2 O 

Totals 
In M.D. 

Difference 



Q7 

' 



"* 11,160 


7 " 


C,. 


0,. 


grammes. 


grammes. 


37-88 


68-56 





13-86 


37-88 


82-42 


39-06 


81-24 



= 8744:- 



-1-18 



+ 1-18 



H 2 . 

grammes. 

2-91 
1-73 

4-64 
4-80 

-0-16 



N 2 . 
grammes. 

19-59 



19-59 
19-29 

+ 0-30 



Experiment 1496. At a density of 0'5 a charge of 155 "84 grammes of cordite 
were fired under a pressure of 52 '84 tons per sq. inch (80547 atmospheres). On 
firing, a slight escape of gas passed the firing plug, which, however, became 
immediately tight. The quantity of gas measured was 93,1 99 - 8 cub. centims., when 
reduced to C. and 760 millims. pressure. 21 '135 grammes of water were collected, 
representing 26,291 cub. centims. aqueous vapour. At the standard temperature 
and pressure, the gas analysis was as follows : 





I. 


II. 






Percentage 




Total, grammes. 




volumes, 


Total, permanent gases. 






permanent gases. 










cub. centims. grammes. 




C0 2 . . 


41-95 


39,097-3 = 77-06 




CO ... 


19-10 


17,801-2 = 22-32 




H . . . . 
CH 4 . . . 


12-05 
7-05 


11,230-6 = 1-01 
6,570-6 = 4-71 


-149-49 


N . . . . 


19-85 


18,500-2 = 23-25 




H 2 . . . 





21-14 


- 



216 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



If the column of weights be added up, it will be found that there is a deficiency of 
6 '3 5 grammes. The quantity of gas measured must therefore be increased to 
97,158-9 cub. centims., and the corrected calculation will stand thus: 





I. 


II. 


III. 


IV. 




Percentage 
volumes, 


Total, permanent gases. 


Percentage 
volumes, 


Percentage 
weights, total 




permanent gases. 




total gases. 


gases. 




cub. centims. grammes. 






CO, . . . 


41-95 


40,758-2 = 80-38 


33-02 


51-84 


CO ... 


19-10 


18,557-3 = 23-29 


15-03 


15-03 


H . . . 


12-05 


11,707-7 = 1-04 


9-48 0-67 


CH 4 . . . 


7-05 


6,849-7 = 4-93 


5-55 3-18 


N . . . 


19-85 19,286-0 = 24-26 


15-62 


15-65 


H,0 . . . 





27,408-4 = 21-94 


21-30 13-63 


Total gases .... 


124,567-3 =155-84 









RECONCILIATION. 





C,. 


2 . 


Hg. 


N 


C0 2 . . . 
CO ... 
H . . . 

CH 4 . . . 

N . . . 


4195 
0-1910 
0-1205 
0-0705 
0-1985 


0-2098 
0-0955 

0-0353 


0-4195 
0-0955 


0-1205 
0-1410 


0-1985 


0-3406 0-5150 0-2615 0-1985 


x!2 x!6 x!4 


=4-087 8-240 0-2615 2-779 



Multiplying again by 



H 2 

Totals 
Originally in cordite 



J 11,1607 








grammes. 
35-58 


O 2 . 

grammes. 

71-73 
19-50 


H 2 . 
grammes. 

2-28 
2-44 


N 2 . 
grammes. 

24-19 


35-58 
35-65 


91-23 
90-69 


4-72 
4-68 


24-19 
24-05 



-0-07 



+ 0-54 



+ 0-04 



+ 0-14 



The heat units evolved by the explosion were, as has been already mentioned, 
determined in a calorimeter of the type of that described by Professor OSTWALD in 
his " Physico-Chemical Measurements." 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



217 



The heat capacities of the explosion vessels were carefully determined, as were 
those of the calorimeters and their equipage, including the stirrers and the mercurial 
thermometers. The latter were of the differential type described by Professor 
OSTWALD, those I used having a range of about 8 C. Two observations for each 
density were sufficient if the observations were accordant. If not accordant, three 
were generally taken. 

Not unnaturally, the observations at the higher densities were considerably more 
accordant than those at the lower. 

Commencing with the Chilworth R. R. nitrocellulose (tubular) in Experiment 1344, 
9'17 grammes were fired, the explosion vessel, when fired, being suspended in 
4000 grammes of distilled water in the calorimeter, the water equivalent of the 
explosion vessel and the calorimeter being 680 cub. centims. It was then found that 
immediately before explosion the calorimeter differential thermometer showed 1'1G1 
(equivalent to 19 '9 C.). 





Degrees Cent. 


Difference. 


Temperature before explosion 


1-161 




2 minutes after explosion . . . 


2-600 





4 ... 


3-043 




6 ... 


3-055 




8 


3-057 








- -002 


10 ,, 


3-055 








- -003 


12 ,, 


3-052 








- -001 


i) 14 >, ,, >, 


3-051 








- -003 


16 ... 


3-048 








- -004 


18 ... 


3-044 








- -002 


20 ... 


3-042 





C. 

It will be observed that the maximum temperature reached was. . 3 '057 
Subtracting temperature before explosion 1'161 

we have 1'896 

Adding correction for lost heat during rise 0'010 

1-906 
Hence ^ = 9727 heat units. 



VOL. CCV. A. 



2 F 



218 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



The temperature of the water in the outer vessel did not move during the 
experiment, being 21'0 C. before and after. 

A second determination of the heat, developed under the same conditions, was 
made in Experiment 1345, which was simply a repetition of Experiment 1344. Here, 
immediately before explosion, the differential thermometer gave a temperature of 
0722 (equivalent to 19'4 C.). 





Degrees Cent. 


Difference. 


Temperature at moment of explosion .... 


0-722 




2 minutes after explosion . . . 


2-050 




4. 

11 11 11 


2-575 




6 ... 


2-604 




,. 11 11 it ... 


2-618 








-001 


iv -. ,, ,* ... 


2-617 








- -003 


19 
11 * 11 11 11 ... 


2-614 








-002 


11 11 11 ... 


2-612 








-003 


-| r> 

11 11 11 11 ... 


2-609 





Here the maximum temperature reached in 8 minutes was 
Subtracting temperature before explosion 



Correction for loss of heat 



C. 

2-618 
0722 

l-896 
0'009 

1-905 



Hence units of heat developed = 4680x1 ' 905 = 972 '2 units. 

9'17 



The previous experiment having given 9727 heat units, the mean may be taken 
as 972'5. It is unnecessary to say that this degree of accuracy is exceptional, but 
still, considering the nature of the experiments, the accuracy, even at moderate 
densities, cannot be considered unsatisfactory. 

Thus in Experiment 1392, at a density of 0'25, 7737 grammes of M.D. were fired, 
the differential thermometer being at 2'012 (equivalent to 18'3 C.). Hence 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



219 





Degrees Cent. 


Difference. 


Temperature at moment of explosion .... 


2-012 




93 


2 minutes after explosion . . . 


3-510 




) 


4 
j ... 


3-707 







6 ... 


3-721 







8 ... 


3-721 










- -002 


>i 


10 ... 


3-719 










- -003 


>) 


12 ... 


3-716 










- -002 


n 


14 


3-714 










- -003 


i) 


16 


3-711 





C. 
. . 3721 

. . 2'012 

1-709 
Correction 0'011 



Hence maximum temperature reached . 
Less 



1-720 



TT ., f , 4680x1-720 , nono 
Hence units ot heat = = 1039 '2 units. 



7737 



The repeat Experiment 1393 gave 



TT -4. c v, 4. 4680x1-720 iriOAO , 

Units of heat = = 1030 '2 units. 

7'737 

Again, in Experiment 1390, at the same density, 0'25, the same number of grammes 
were fired, the differential thermometer immediately before the explosion being at 
0-581 (equivalent to 18 "6 C.). Hence : 





Degrees Cent. 


Difference. 


Temperature at moment of explosion .... 


0-581 




n 


2 minutes after explosion . . . 


2-362 




11 


4 ... 


2-599 




ii 


6 ... 


2-617 




ii 


8 ... 


2-618 










- -004 


n 


10 ... 


2-614 










- -003 


ii 


12 ,, ... 


2-611 










- -004 


ii 


14 ... 


2-607 










- -004 


n 


16 ... 


2-603 





220 SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 

C. 
Hence maximum temperature reached . . . . 2 '6 18 

Less 0-581 



2'037 
Add correction . 0'012 



2'049 

TT ., ,., 4680x2-049 10QQ K 

Hence units of heat = = 1239 '5. 

7737 

The repeat Experiment No. 1391 gave 

TT ., , 4680x2-060 

Units of heat = ^^ = 1246'2. 

To illustrate the remark I made as to increase of accuracy when taking the calorimetric 
observations at the higher densities, I give the whole of the observations on this point 
with Mark I cordite. Thus, at the density of 0'05 the three observations were, 
respectively, 1265'!, 1303'0, 1248'8, or a mean of 1272'3 units. With density O'l the 
three observations were 1275"8, 1240'5, 12357, or a mean of 12507 units. Density 
0-15 gave 12597, 1247'2, 12427, or a mean of 1249'9. With density 0'20, 1245'2, 
1246-5, 1241-0, or a mean of 1244'2. Density 0'25, 1246'2, 1239'5, and 1241'3, giving 
a mean of 1242'3. 0'3 density gave 1276*9, 1280'0, 1264'0, mean 1273'6 : for 0'4, 
1305-0 and 1294'3 or 12997 mean, and for 0'45, 1326'3 and 1320'0 or mean 1323'2. 

We are now in a position to give in a tabular form the result of the series of 
experiments on the three explosives fired under a variety of densities and pressures, 
and with regard to which the essential constants have been determined. 

These tables give : 

(1.) The densities under which the various charges were fired. 

(2.) The volumes of permanent gases generated at C. and 760 millims. of 
barometric pressure per gramme of explosive. 

(3.) The total volume of gas per gramme, aqueous vapour being included. 

(4.) The percentage volumes of permanent gases. 

(5.) The percentage volumes of the total gases. 

(6.) The percentage weights of the total gases. 

(7.) The pressures at each density in tons per sq. inch. 

(8.) The same pressures in atmospheres. 

(9.) The units of heat determined, the water being fluid. 
(10.) The imits of heat, water being gaseous. 

(11.) The specific heat of the products of explosion for each density. 
(12.) The comparative temperatures of explosion determined by dividing the 

units of heat (water gaseous) by the specific heats in (11). 

(13.) The comparative potential energy, the highest energy determined being 
taken as unity. 



SIE ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



221 



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m o m m m 

02 r-H O O 00 


01 eo oo in en o 

o o * m to co 


* co t~ oo 10 co 

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oo o 

CO ^^ 
CN O 
Oi 00 O O CM 'Ji O 


<M O5 

<o t- 


r-H O3 CM t- OS 
-^ I 1 I 1 r-H 


co m 02 in m ^H 

CO i i i i CM 


.-i in o co 10 co 

IO r i i i > i 


CT CO O t- O rH 
IO CO 00 2 

o eo c-j 

rtrt S 


* O5 O 


o in o m o 

CO CD OO O CM 


CO i i ^ t- O in 

r ' 00 CO CJ2 i 1 CO 


00 IN in * 1- ^ 
CD CO OO CO in CM 


oo 

CO t- 
CO t- 
CM to 
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oo CM * in o> 

CO IN r-H r-H 


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CO I 1 r 1 r 1 CM 


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to~~ g 


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Density of charge explc 
Volumes of permanent g 
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Percentage volumes of 
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222 



SIE ANDEEW NOBLE : EESEAECHES ON EXPLOSIVES. 



1C 
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OO CM O OO CM O 

o o m oo co CM 


oo 

r-H CO 
^J< t~ 
CO r-H 
CM O t- t- CM Cl OO 


O C5 in 
CO 1 1 
r- Oi 


CO CD i 1 CO -* 
CM CO <M r-H 


o o oo <M IM m 

r-H CO r-H r-H r-H 


CD in r-H 1 1 -^ r-H 
CO CO r 1 r I 


in t- -* ^* o o 

I-H ^H CO t- 
CO O C34 '~ l 
CM r-H 
^^ 


in 

i i O OO 


00000 

m cs t o o 


in oo m o> co o 
o^ ^ ci m m in 


O r-H CO CD O5 OO 

co I-H t~ o co in 


O 

-* O5 

oo o 

CO CM 

<M OO t- CO CM 00 OO 


O O CO 
O CO 
t OS 


r-H OO CM r-H in 

CM CO <M r-H 


t~ (M X r 1 <M CO 

T-H CO r-H r-H r-H 


CM OO r-H r-H -^ r-H 
CO CO r-H ^H 


O -* * <M O ?- O 

r-H in r-H in !2 

inoo | 


o 

r-H -* ^ 


o o o o o 

r-H J^ i O r-H 


-* O * CO t~ (M 
t~ O5 <M 00 in t 


CM r-H i 1 in *^ t 

co t~ co in t~ m 


CM 

in CM 

m oo 

CO <M 
C5 OO OO * <M ir- OO 


O CO CD 
OO * 
- 


O O CO r-H in 

CM -* <M r-H 


CD CO C2 O <M CD 
r-H CO r-H r 1 1 1 


O C5 r-H O -* CM 
CO CO I-H r-H 


CD r-H cs CM o ;_ o 
m CM co 50 

03 W 




1O 

O 00 **< 


in o in in in 

r-H CO r-H CO t- 


in t^ m Ci o^ in 

OO 00 OS CM OO r-H 


C3 00 CM OO <M i-H 
CO CO CO r-H CO 00 


-* 

r-H r-H 

t- O 

CO -* 
1^ CO O5 O3 CM CM OO 


O r-H in 

oo m 
i- Oi 


oo c^ co o m 

r-H TH O5 r-H 


*f * 00 O (M OO 
r-H CO r-H r-H i 1 


J^ r-H r-H O O CO 
CM * r 1 1 1 


CM r-H in r-H O O 

r-H CO CO Jg 

^,00= g 

^* 












o o 
. % . ^ 
13 W) 

rS ' 


gBwgfc 


OOr-HMH, 1 ^, 

oO w o^W 


OOffiKrO 

oO ffi o^B 


^ 1 1 

S "Go g a 


12 +3 02 


, , 


. , 


, j 


m'3 9 -fi a5 


Density of charge explc 
Volumes of permanen 
per gramme . . . 
Volumes of total ga 
gramme .... 


Percentage volumes of 
permanent gases 


Percentage volumes of _ 
total gases . . . * 


3 ' 

1 ' 
^ 

a 

b OQ 
O 

J>| 

S3 

1* 


.4, S S e 8 * 

ffgw M o-. 

fe -g, S fe fl 

O r*H-M 4-1 oj tn 
P< CO -g r* ^ O 

al^S -B^ 
<^ftfle 

.S.sJ,SjB-l 
S'S'S o | g 

C2 S 

g 53 M ao rs a, et, 

ra S .-g .-g o a a 

iisim 





O 

O 
Q 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



223 



in 

** OS CO 


o in in o o 

O CO CO I-H -* 


co o * in co o> 

l-H (M IO <M l-H CO 


co CM os in * -^ 
CM os t- * m o 


oo 

CM CO 

oo oo 

CM CO 

in co os t- CM os t- 


o o co 

00 1-H 

to co 


m t CM i-H co 

CO CM 1-H r 1 1 


OS CO O OJ I-H CO 

<M (M 1 1 1-H l-H 


t~ CO O IO r-H I-H 

-* CM 1-H 1-H 


CO CO t- O 

-* t- co t- S3 

^H OS 

^^ 5h 


o 

* I-H 00 


o in in o o 
* CM -* co co 


CO I-H -^ 10 O t 
OO t-~ CO ^" <^ CO 


co oo o in m cs 
oo t~ os co co i i 


OS 
CO O> 

oo in 

tN CO 

os o **< ^< CM os t- 


000 
OS -* 

co oo 


CO t- <* OS IO 
CO <M 1-H 1-H 


t- <N C^I !> CO CO 

(M (M l-H l-H l-H 


in CO O -* CO r-H 
* CM f-H l-H 


-* O l-H l-H O 1- O 

CO CM CM CO 

CO OS 

in rH N 


o 
co os CM 


CO CM CO i i ID 

O O r-H -* CO 


t- co in o i~- 10 

-* * CO (N I-H CO 


O OO CM CO 10 OS 
CM OS i-H OO CO -^ 


<M 
CM OS 

* CO IO 

o o m os CM 1-1 t~ 


O t- <M 

co oo 

t- 00 


00 * t- t~ CO 

CM CO r-H r-H 


CO OO * CO r-H D 
C^ (M 1-H 1-H 1-H 


O O r-H CO CM i-H 
T^ CO I-H r-H 


O -H CM OO O 
CM CO I- i-H CO 

I-H 02 os J 

CO ^ 
CO 


03 
CM OO IO 


o o o o m 

OO CO r-H CO >*< 


CO OO O CO t- CO 
i 1 -* <M O ^H OS 


i 1 CM CM CM CO t 

l-H -H^ , 1 00 CO ^H 


co 

CM OO 

r-H CO 
CO 1O 

IO * CM CO CM CM t- 


O C- 00 

co oo 
t~ oo 


r- -* t- r- co 

CM CO r- 1 r-H 


CO OO -* CO i-H CO 

Cq CM r-H l-H l-H 


O l-H l-H CO CM l-H 
>* CO l-H l-H 


1-H t~ O OO O 

CM r~ t- ^H co 

CM OS OS 25 

g 


CM 

CM 

CM CM CO 


O IO IO O O 

r-H in CM t- -* 


CO OS t~ t~ CO 00 
CO O CO 00 O CO 


00 IO CO C-l O CO 

oo ^H co in m m 


-* 

10 oo 
in co 

1>- CO -* 
* CO O OS CM t~ t- 


O OS CM 

in CM 

t- OS 


IO CO O -* CO 
CM CO CM I-H 


O O CO CO I-H t- 
<M CO I-H i i i 


CO **< i I CM CM (M 

CO CO I-H l-H 


CO O r-H CO O J_ O 

I-H I-H co co : 
in os co 3 

^ CO 



CM OS OS 


o o 10 o m 

os co j~ in o 


-*f OO OS OS OS i 1 
OS O C5 CO t~ CO 


CO -* CO C-1 CM 00 

^ i i ^t< os in -^ 


CM 

-* OO 
CO CO 
r-i CO CO 
-* CO CO -* CM 00 t~ 


O OO 05 
CO CM 
t- OS 


CM 00 r-H CO CO 

CM CO CM I-H 


OO <M t- CM O t- 

I-H CO I 1 I-H 1 1 


** t- r- 1 i i cq CM 

CO CO ^H i-H 


* co os CM o o 
I-H os <M co r 

I-H OS 00 

g 


10 

l-H -^ i-H 


in m m o m 

OO CO CO O3 t- 


t~ IO CO CO CM (M 
CO GO GO IO CD t~ 


OO I-H X) t~ * <M 

i I OS CO O IO CO 


1 I 
I- O 
OO CM 
CO CM 

* co co CM CM os L^ 


o -* o 
O fr- 
ee os 


O O CO T 1 CM 
CM -* <M i-H 


t~ CO O5 I 1 O CO 
i-H CO r 1 i ' I-H 


(M OS i-H r-l CM CM 

CO CO i 1 i I 


o m t- o o ' o 

i 1 OO CO CM *2 

in 'W co ^ 


o 

( oo co 


in in o m m 

OO -* O5 GO O5 


oo CM t~ I-H m J^- 

-* -* CO t- t- OS 


CO -* CO 00 CM t- 
O CM t- ^*< OS IO 


OS 

CO ,-H 

co in 

CO CO CM 
CM CM CO * CM t- t- 


o * 01 

O CO 

OO 05 


OS i 1 -* O <^l 

1-H -* (M rt 


CO -* O O O CO 
i-H CO CM r-l i 1 


r-H l-H 1-H O CM CM 
CO ^ l-H l-H 


CO -^H O5 <M O !_, O 

in co o 

OS =0 CO %> 
CO 


1O 
O Jr- I-H 


o in o o in 

OJ -* -* CO CO 


OO CO I-H OS OS O 
CO CO O -* I-H O 


OS CO ^ "^ r-H OS 
I-H IO t^ CO t -* 


CM 

t- OS 

t- CO 
IO CO CO 
CO t^- I-H CM CM r-H t^ 


O -* co 

1-H OS 

OO OS 


t- CO -* O CO 

^H & (M l-H 


* in O O r-H OO 
r-H CO CM l-H 1 1 


OO CO i-H O CO CM 
CM * r-H r-H 


CO O CO OS O O 

r-H OS CM J 

IO CO OO 

"^T 1 

CO 












li ' ,' 

T3 . & . 

HI 8 


6o K Kft 

QO^o 


d'Offiffitz^ 

o w s^w 


gSwgfcg 


31 - ^ 1 -2 -s 
o a cs to c 

g s^ II 


x S 2 


t J 


. 


^ , 


^ "ft M S, 


Density of charge e 
Volumes of pe 
gases per gramn 
Volumes of total g 
gramme 


Percentage 
volumes of per- - 
manent gases 


Percentage 
volumes of total - 
gases 


o "o 

SpS 

j -4-1 OT 

T^ o w 

H O3 

ir 

^ 


8 a if * 

I^J , ."s . 

-^ -^ .j'' 5 CQ 

c8 -g j_, o> co 

c c Si fl.fc 
"- 1 .9 ^a fs co 2 5 -3 ^ 

CO .CO-rHS- ia 1s=h 

Nils Si III 

rhs~m^ 



P 

- 
- 
- 



224 SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 

If the figures given in these tables be carefully examined, it will be observed that 
in the three explosives the transformation on firing appears in all to follow the 
same general laws. 

Thus in all three there is, with increase of pressure, at first a slight increase, 
afterwards a steady decrease in the volume of permanent gases produced. 

This increase in the total gases is much less marked with cordite, and in the case 
of M.D. and nitrocellulose there is practically a steady decrease in the volume of 
the total gases. 

In all three explosives there is, with increased pressure, a large increase in the 
volume of carbonic anhydride and a large decrease in the volume of carbonic 
monoxide. 

In the case of hydrogen, this decrease of volume with increase of pressure is very 
great, while with methane, the percentage which with low pressures is quite 
insignificant, very rapidly increases and at the highest density is from twenty to 
thirty times greater than the lowest density. 

There are some variations in the percentages of nitrogen and H 2 O, but on the 
whole these constituents may be considered to be nearly constant. 

The units of heat with a slight decline at first afterwards increase and somewhat 
rapidly at the highest pressures. 

But the changes which take place under different pressures are more readily 
appreciated if the observations are graphically recorded by means of curves. 

Accordingly in Plate 5 I have given for three explosives the pressures in tons per 
sq. inch and in atmospheres, deduced from the experiments under consideration, 
and which pressures vary from about 3 tons per sq. inch (457 atmospheres) to (in 
the case of Mark I cordite) 53 tons per sq. inch (8078 atmospheres). 

It will be observed also that from densities of about 0'25 upwards the curve 
expressing the relation of pressure to density, both in the Mark I cordite and in the 
M.D., differs inappreciably from a straight line. This remark also appears to be, in 
some degree, corroborated by an experiment I once made at a density of unity, and 
which gave a pressure of about 112* tons per sq. inch (17,070 atmospheres). 

With nitrocellulose there appears, at high densities, to be a tendency to detonate, 
from which tendency Mark I cordite appears to be free. By way of showing the 
enormous superiority of the new explosives as regards potential energy, I have added 
to Plate 5 the curve showing the relation of pressure to density of fired gunpowder. 

In Plate 6 there are three sets of curves : (l) The changes in the volumes of the 
permanent gases due to increase of density ; (2) The changes in the volumes of the 
total gases which do not differ very greatly from those of the permanent gases ; and 
(3) The changes in the units of heat at different densities (water fluid). 

It may be noted that, while at pressures under 20 tons per sq. inch the heat 

* On the occasion referred to, I was not sure that the pressure might not be higher, as there was 
considerable friction between the piston and the cylinder, due to compression of the gauge. 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 225 

developed does not vary greatly ; at higher pressures the heat increases considerably, 
thus compensating for the loss of potential energy due to the decrement in the volume 
of gas generated. 

Plates 7, 8 and 9 show graphically the great changes that take place in the 
decomposition of the gases in passing from densities of 0'05 to 0*45. 

In all, carbon monoxide and dioxide change places, the two gases having equal 
volumes in the case of cordite 24'2 per cent, at a density of 0'19, in the case of M.D. 
25 '5 per cent, at a density of 0'32, and with nitrocellulose 26 per cent, at a density 
of 0-36. 

The changes with hydrogen and methane are equally striking, the hydrogen in 
cordite falling from a maximum of nearly 16 per cent, in volumes to about 9 '5, while 
the methane increases from about 0'2 per cent, to about 5 '5 per cent. In M.D. the 
volumes of hydrogen fall from about 19 per cent, to about 10 '4 per cent., while the 
volume of methane increases from about 0'3 per cent, to nearly 9 per cent., and in 
nitrocellulose the volume of hydrogen falls from 207 per cent, to about 11 per cent., 
the methane increasing from 0'5 per cent, to a little over 9 per cent. 

In the tables I have submitted it will be observed that the specific heats and the 
temperatures of explosion have been given, but in regard to temperatures so far 
above those in regard to which accurate observations have been made the figures I 
give can only be taken as provisional. The specific heats of the various gases have 
been taken at the values usually assigned to them. Of course, it cannot be assumed 
that these specific heats remain unchanged over the wide range of temperature 
necessary, although I believe it has been found that the specific heats of some 
permanent gases such as nitrogen and oxygen are but slightly altered up to 800 C. 

The temperatures of explosion which, as I have said, can only be taken as 
provisional, have been obtained by dividing the units of heat (water gaseous) by the 
specific heats, and, although provisional, can safely be used in comparing the 
temperatures of explosion of the three explosives. The temperatures of explosion, for 
example, of cordite and nitrocellulose at the density of 0'20 may tolerably safely be 
taken to be in the ratio of 51 to 36. 

I am, from other considerations, inclined to believe that the temperatures I have 
obtained and given in the tables are not very far removed from the truth. I tried with 
cordite to confirm the results by using the equation of dilatability of gases. At the 
high pressures the results were satisfactory, but quite the reverse at the lower 
densities. 

The comparative approximate potential energies are obtained by multiplying the 
volume of gas produced by the temperature of explosion. The means for the three 
explosives are respectively: cordite, 0'9762 ; M.D., 0'8387 ; nitrocellulose, 07464. 
The highest potential energy (taken as unity), it will be noted, was obtained from 
cordite at a density of 0'5. 

I submit that the wide differences in the transformation of the three explosives 

VOL. OCV. A. 2 G 



226 SIR ANDEEW NOBLE: RESEARCHES ON EXPLOSIVES. 

with which I have experimented justify the conclusion at which Sir F. ABEL and I 
arrived with respect to gunpowder, viz., that any attempt to define by a chemical 
equation the nature of the metamorphosis which one explosive may be considered to 
undergo would only be calculated to convey an erroneous impression as to the definite 
nature of the chemical results and their uniformity under different conditions. 

The apparatus shown in Plate 4 was employed for two purposes, (l) to determine 
the time for the complete ignition of various explosives, or for various forms and 
thicknesses of the same explosives ; (2) to determine the rate at which the exploded 
gases part with their heat to the walls of the vessel in which they are enclosed. 

The high and low speeds that can be given to the drum permit these two 
observations to be made by a single experiment. Thus, in Plate 10, I show the 
commencement and part of the curves of two experiments, the one (fig. 1) fired at a 
pressure of a little over 12 tons per sq. inch (1829 atmospheres), the other (fig. 2) 
nearly 18 tons (2744 atmospheres). At the point "A" the charge is fired, and it will 
be noted that the circumference of the drum is travelling at about 40 inches per 
second. From fig. 2 it will be seen that at 2 seconds after firing the speed has, in 
this experiment, been reduced to about an inch per second. 

The times required for the completion of ignition are given in Plate 11, and are 
obtained from the curves shown on Plate 10 and from two similar curves. The 
vertical scale in Plate 11 for the three last densities is doubled to make them accord 
with density O'l, the spring employed in that experiment being half the strength of 
that used for the last three. 

I may point out that when fired in close vessels the rate of combustion of the 
explosives, even in the cord form, appears to be very constant, the increase of pressure 
apparently nearly compensates for the reduction of surface, the differences in time 
of burning being due to want of uniformity in the lighting, which in many cases is 
very variable. This is illustrated by comparing the times of ignition of densities O'l 5 
and 0'2 in Plate 11, where the total time from firing to complete ignition is less for 
density O'l 5 than for density 0'2. In reality, however, after complete lighting the 
latter is burning quicker, as may be seen by comparing the angles made by the 
curves with the axis of abscissae. 

But this question is too large to enter into fully in the present paper. I therefore 
only give the times of approximate complete combustion of cordite and M.D. cordite 
of different diameters when exploded at a pressure of about 9 tons on the square inch. 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



227 



Diameter of 
cordite. 


Time of burning, 
seconds. 


Diameter of 
M.D. 


Time of burning, 
seconds. 


0-033 


0-0163 






0-045 


0-0172 








0-091 


0-0207 








0-181 


0-0274 


0-192 


0-0377 


0-266 


0-0337 


0--235 


0-0480 


0-343 


0-0395 


0-263 


0-0547 


0-482 


0-0499 


0-318 


0-0679 


0-577 


0-0570 





' 



Comparing the times of burning of 0'2 cordite and rifle cordite, the times are 
approximately as follows : 



0-2 cordite. 


Rifle cordite. 


Tons 
per sq. inch. 


Seconds. 


Tons 
per sq. inch. 


Seconds. 


3-5 
10-0 
11-5 


0-03844 
0-01896 
0-01700 


3-5 
10-0 
11-5 


0-00972 
0-00553 
0-00498 



The rates of cooling of cordite (charges and densities being as stated) are shown in 
Plate 12, the interior surface of the explosive vessel being 54'9 sq. inches (354'3 sq. 
centims.). The communication of heat to the vessel is extraordinarily rapid. The 
pressure and approximately the temperature of the exploded gases is in the case of 

Density O'l (32 grammes) reduced to one half in 0'87 second, and to one quarter 
in 270 seconds. 

Density O'l 5 (48 grammes) reduced to one half in 0'93 second, and to one quarter 
in 2 '8 2 seconds. 

Density 0'20 (64 grammes) reduced to one half in 1'54 seconds, and to one quarter 
in 3 '8 3 seconds. 

Density 0'25 (80 grammes) reduced to one half in 2'40 seconds, and to one quarter 
in 6 '04 seconds. 

1020'6 grammes of the same cordite fired at a density of O'l in a vessel whose 
interior surface was 3271 sq. centims. reduced its pressure to one half in 3'1 seconds, 
to one fourth in 10 seconds. 

1247'4 grammes fired at a density of 0'12 in the same vessel had the pressure 
reduced to one half in 4'2 seconds, and to one quarter in 13'8 seconds. 

1360-8 grammes fired at a density of O'l 31 in the same vessel recorded a pressure 
of one half in 6 '3 seconds, and of one quarter in 31 seconds. 

2 G 2 



228 



SIR ANDEEW NOBLE: RESEARCHES ON EXPLOSIVES. 



I venture to allude to two other points of interest. I have always thought it 
probable that the dissociation, for example, of carbonic dioxide into carbonic monoxide 
and oxygen might be very greatly modified or extinguished by the extremely high 
pressure at which my experiments have been made ; and I thought it possible that, 
if dissociation did take place, some indication of the re-formation of carbonic dioxide 
would appear in the cooling curves, which have been obtained under a variety of 
conditions and pressures. These curves, however, are singularly free from any 
indication of disturbance, so that, if any recombination does take place, it has no 
effect on the extremely regular coolings to which I have alluded, and would seem to 
prove that the re-formation of CO 2 and H 2 O must take place gradually and in no case 
per saltum. I have found also, and this point is of some interest, that gases I have 
taken from the chamber of a 9 '2-inch gun immediately after firing have, when 
corrected for the air with which they are mixed, the same composition as those which 
have been fired under similar densities in a close vessel. 

The experiments I have made on erosion with the three explosives referred to in 
this paper, and on some others, have satisfied me that the amount of absolute erosion 
is governed practically entirely by the heat developed by the explosion. I had 
thought that increase of pressure would considerably increase the amount of erosion, 
but in experiments carried on with cordite and nitrocellulose under pressures varying 
from 5 tons to 32 tons per sq. inch the erosion was practically entirely independent 
of the pressure both for the cordite and the nitrocellulose. The results of these 
experiments are given in Plate 13. 

APPENDIX. 

Abstract of Experiments Referred to in Paper. 

CORDITE MARK I. 

Experiment 1380. Fired in explosion vessel Q, 16 '75 grammes of Mark I cordite. Density of 
charge - 05. 

Pressure 2-9 tons per sq. inch (442 -1 atmospheres). 

Permanent gases 11,186-7 cub. centims. at C. and 760 millims. 

Aqueous vapour 3296 6 cub. centims. 

RECONCILIATION. 





C. 


0. 


H. 


N. 


Found by analysis .... 
Originally in cordite . . . 


grammes 

3-72 
3-68 


grammes 
9-47 
9-35 


grammes 

0-47 
0-48 


grammes 
2-91* 
2-48 


Differences .... 


+ 0-04 


+ 0-12 


- o-oi 


+ 0-43 



* The N and contained in air in cylinder not taken into account. 



SIE ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



229 



Experiment 1383. Fired in explosion vessel Q, 32-73 grammes of Mark I cordite. Density of 
charge 0-10. 

Pressure 7 -8 tons per sq. inch (1189-0 atmospheres). 
Permanent gases 23,124-7 cub. centims. at C. and 760 millims. 
Aqueous vapour 6277 -2 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


0. 




Found by analysis .... 
Originally in cordite . . . 

Differences .... 


grammes 

7-66 
7-53 


grammes 

19-26 
19-13 


+ 0-13 


+ 0-13 



H. 



grammes 

0-98 
0-98 



0-00 



N. 



gram tnes 

5-56 

5-08 



+ 0-48 



Experiment 1386. Fired in explosion vessel Q, 47 -77 grammes of Mark I cordite. Density of 
charge 0-15. 

Pressure 11-49 tons per sq. inch (1751-5 atmospheres). 
Permanent gases 33,646-2 cub. centims. at C. and 760 millims. 
Aqueous vapour 9104-7 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


H. 


N. 


Found by analysis .... 
Originally in cordite . . . 


grammes 

11-14 
11-20 


grammes 

28-26 
28-48 


grammes 

1-44 

1'47 


grammes 

7-98 
7-56 


Differences .... 


- 0-06 


- 0-22 


- 0-03 


+ 0-42 



Experiment 1371. Fired in explosion vessel Q, 63 -96 grammes of Mark I cordite. Density of 
charge 20. 

Pressure 17 -2 tons per sq. inch (2621-9 atmospheres). 
Permanent gases 46,440-3 cub. centims. at J C. and 760 millims. 
Aqueous vapour 11,594-1 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


H. 


N. 


Found by analysis .... 
Originally in cordite . . . 


grammes 

15-45 
15-02 


grammes 

38-59 

38-18 


grammes 

1-98 
1-98 


grammes 

10-86 
10-14 


Differences .... 


+ 0-43 


+ 0-41 


o-oo . 


+ 0-72 



230 



SIR ANDEEW NOBLE: RESEARCHES ON EXPLOSIVES. 



Experiment 1389. Fired in explosion vessel Q, 80-3 grammes of Mark I cordite. Density of 
charge 25. 

Pressure 21-08 tons per sq. inch (3213-3 atmospheres). 
Permanent gases 55,834 '4 cub. centims. at C. and 760 millims. 
Aqueous vapour 14,480 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


H. 


N. 


Found by analysis .... 
Originally in cordite . . 


grammes 

18-69 

18-76 


grammes 

47-33 

47-70 


grammes 

2-40 
2-46 


grammes 
13-17 
12-67 


Differences .... 


- 0-07 


- 0-37 


- 0-06 


+ 0-50 



Experiment 1375. Fired in explosion vessel Q, 95-94 grammes of Mark I cordite. Density of 
charge 30. 

Pressure 30'5 tons per sq. inch (4649 -3 atmospheres). 
Permanent gases 64,453- 7 cub. centims. at C. and 760 millims. 
Aqueous vapour 16,653-4 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


H. 


N. 


Found by analysis .... 
Originally in cordite 


grammes 

22-11 
22-31 


grammes 

56-35 
56-71 


grammes 

2-88 
2-93 


grammes 

15-12 
15-05 


Differences .... 


- 0-20 


- 0-36 


- 0-05 


+ 0-07 



Experiment 1497. Fired in explosion vessel Q, 124-67 grammes of Mark I cordite. Density of 
charge 0'40. 

Pressure 41 -4 tons per sq. inch (6310-8 atmospheres). 
Permanent gases 80,403-1 cub. centims. at C. and 760 millims. 
Aqueous vapour 21,832 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


O. 


H. 


N. 


Found by analysis .... 
Originally in cordite . . . 

Differences .... 


grammes 

28-54 
28-67 


grammes 

72-79 
72-89 


grammes 

3-74 
3-76 


grammes 

19-36 
19-35 


- 0-13 


- 0-10 


- 0-02 


+ o-oi 



SIR ANDEEW NOBLE: RESEARCHES ON EXPLOSIVES. 



231 



Experiment 1496. Fired in explosion vessel Q, 155-84 grammes of Mark I cordite. Density of 
charge 0-5. 

Pressure 52-84 tons per sq. inch (8063 '8 atmospheres). 
Permanent gases 97, 158- 9 cub. centims. at C. and 760 millims. 
Aqueous vapour 26,291 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 




Found by analysis .... 
Originally in cordite . . . 

Differences .... 


grammes 

35-58 
35-65 


1 


- 0-07 


- 



0. 


H. 


N. 


;rammes 
90-52 
90-69 


grammes 

4-63 
4-68 


grammes 

24-19 
24-05 


0-17 


- 0-05 


+ 0-14 



Experiment 1387. Fired in explosion vessel Q, 16 grammes M.D. Density of charge 0-05. 

Pressure 2 -7 tons per sq. inch (411-6 atmospheres). 

Permanent gases 12,899-8 cub. ceYitims. at C. and 760 millims. 

Aqueous vapour 2861 -2 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


H. 


1 


Found by analysis .... 
Originally in M.D 


grammes 

4-24 
4-66 


grammes 

9-34 
9-53 


grammes 
0-53 
0-53 


gnu 

2 
1 


Differences .... 


- 0-42 


- 0-19 


o-oo 


+ 



N. 



2-55* 
97 



* Chiefly due to air in explosion vessel. 

Experiment 1388. Fired in explosion vessel Q, 31-98 grammes M.D. Density of charge 0-10. 
Pressure 6 -9 tons per sq. inch (1051-8 atmospheres). 
Permanent gases 25,621-0 cub. centims. at C. and 760 millims. 
Aqueous vapour 5145-1 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


H. 


N. 


Found by analysis .... 
Originally in M.D 


grammes 
8-51 
9-12 


grammes 
18-53 
18-66 


grammes 

1-04 
1-03 


grammes 

4-85* 
4-49 












Differences .... 


- 0-61 


- 0-13 


+ 0-01 


+ 0-36 



Including N in air. 



232 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



Experiment 1357. Fired in explosion vessel Q, 47 '97 grammes M.D. Density of charge 0-15. 
Pressure 10-2 tons per sq. inch (1554-8 atmospheres). 
Permanent gases 38,458-3 cub. centims. at C. and 760 millims. 
Aqueous vapour 7600-8 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 0. 


H. 


N. 


Found by analysis .... 
Originally in M.D 


grammes grammes 

13-58 28-00 
13-53 28-13 


grammes 

1-59 
1-66 


grammes 
7-24 
6-69 


Differences .... 


+ 0-05 - 0-13 


- 0-07 


+ 0-55 



Experiment 1356. Fired in explosion vessel Q, 63 -96 grammes M.D. Density of charge 0-20. 
Pressure 15-2 tons per sq. inch (2317'0 atmospheres). 
Permanent gases 50,229 8 cub. centims. at C. and 760 millims. 
Aqueous vapour 9,558-7 cub. centims. at C. and 760 millims. 



RECONCILIATION. 



Found by analysis 
Originally in M.D. 



Differences 



C. 



grammes 

17-17 
17-66 



- 0-49 



0. 


H. 


N. 


grammes 

37-00 
36-74 


grammes 

2-14 
2-17 


grammes 

9-32 

8-74 


+ 0-26 


-0-03 


+ 0-58 



Experiment 1370. Fired in explosion vessel Q, 79 -95 grammes of M.D. Density of charge 0-25. 
Pressure 20'74 tons per sq. inch (3155-4 atmospheres). 
Permanent gases 60,611 -2 cub. centims. at O c C. and 760 millims. 
Aqueous vapour 11,631-4 cub. centims. at C. and 760 millims. 



RECONCILIATION. 





C. 


0. 


H. 


N. 


Found by analysis . . -. . 
Originally in M.D. , 


grammes 

21-21 
21-99 


grammes 

46-17' 

45-74 


grammes 

2-62 
2-71 


grammes 

11-52 
10-8fi 












Differences .... 


- 0-78 


+ 0-43 


-0-09 


+ 0-66 



SIR ANDEEW NOBLE: RESEARCHES ON EXPLOSIVES. 



233 



1354. Fired in explosion vessel Q, 98-94 grammes of M.D. cordite. Density of charge 0'3. 
Pressure 27 '62 tons per sq. inch (4210 3 atmospheres). 
Permanent gases 72,768-0 cub. centims. at C. and 760 millims. 
Aqueous vapour 13,885-5 cub. centims. at C. and 760 millims. 

RECONCILIATION'. 





C. 


O. 


H. 


N. 


Found by analysis .... 
Originally in M D 


grammes 

26-22 
27-05 


grammes 

56-81 
56-26 


grammes 

3-25 
3-33 


grammes 
13-88 
1 V 36 












Differences .... 


- 0-83 


+ 0-55 


-0-08 


+ 0-52 



Experiment 1405. Fired in explosion vessel R, 128-48 grammes of M.D. cordite. Density of 
charge 0-40. 

Pressure 38'1 tons per sq. inch (5807-8 atmospheres). 
Permanent gases 89,410-2 cub. centims. at C. and 760 millims. 
Aqueous vapour 17, 887 '2 cub. centims. at 0' C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


H. 


N. 


Found by analysis .... 
Originally in M.D 


grammes 

33 63 

35 87 


grammes 

73-06 
73-37 


grammes 

4-25 
4-06 


grammes 

17-50 
15-18 












Differences .... 


- 2-24 


- 0-31 


+ 0-19 


+ 2-32 



Experiment 1417. Fired in explosion vessel Q, 143-91 grammes of M.D. cordite. Density of 
charge 45. 

Pressure 43 22 tons per sq. inch (6587 3 atmospheres). 
Permanent gases 97,589-5 cub. centims. at C. and 760 millims. 
Aqueous vapour 19,394-0 cub. centims. at C. and 760 millims. 

RECONCILIATION. 



Differences 



Found by analysis .... 
Originally in M.D. . . 



C. 



grammes 

37-88 
39-06 






- 1-18 



0. 


H. 


N. 


grammes 

82-42 
81-24 


grammes 
4-64 
4-80 


grammes 

19-59 
19-29 


+ 1-18 


- 0-16 


+ 0-30 



VOL. CCY. A 



2 H 



234 SIR ANDEEW NOBLE: RESEARCHES ON EXPLOSIVES. 

Experiment 1339. Fired in explosion vessel L 2 , 41-5 grammes of Rottweil R. R. Density of 

chcirge 0-05. 

Pressure 3-35 tons per sq. inch (510-7 atmospheres). 
Permanent gases 33,811-8 cub. centims. at C. and 760 millims. 
Aqueous vapour 7402-8 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


H. 


N. 


Found by analysis .... 
Originally in R. R 


grammes 

11-26 
11-59 


grammes 

24-49 
23-71 


grammes 

1-44 
1-32 


grammes 
5-79 
4-91 


Differences .... 


- 0-33 


+ 0-7S 


+ 0-12 


+ 0-88 



Experiment 1340. Fired in explosion vessel L>, 83 grammes of Rottweil R. R. Density of charge 0-10. 

Pressure 6 -26 tons per sq. inch (954-2 atmospheres). 

Permanent gases 66,802-6 cub. centims. at 0' C. and 760 millims. 

Aqueous vapour 13,646-7 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


Found by analysis .... 
Originally in R R . . 


grammes 

22 38 
23-17 






Differences .... 


- 0-79 



0. 


H. 


N. 


grammes 

48-60 
47-40 


grammes 

2-81 
2-62 


gramn 

10-8 
9-8 


+ 1-20 


+ 0-19 


+ i-c 



* Partly due to air in explosion vessel. 

Experiment 1341. Fired in explosion vessel Q, 47 97 grammes of Rottweil R. R. Density of charge 15. 
Pressure 10'4 tons per sq. inch (1585-3 atmospheres). 
Permanent gases 38,585-8 cub. centims. at C. and 760 millims. 
Aqueous vapour 7949 -2 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


H. 


N. 


Found by analysis .... 
Originally in R. R 

Differences .... 


grammes 

13-15 
13-39 


grammes 

28-45 
27-40 


grammes 

1-66 
1-52 


grammes 

6-17 
5-38 


- 0-24 


+ 1-05 


+ 0-14 


+ 0-79 



SIR ANDREW NOBLE: RESEARCHES ON EXPLOSIVES. 



235- 



Experiment 1342. Fired in explosion vessel L.>, 166 grammes of Rottweil R. R, Density of charge 20. 
Pressure 14-41 tons per sq. inch (2196-6 atmospheres). 
Permanent gases 127,643-1 cub. centims. at C. and 760 millims. 
Aqueous vapour 26,721 -6 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


II. 




Found by analysis .... 
Originally in R. R. . 


grammes 

44-7 
46-6 


grammes 

96-5 
95-6 


grammes 

5-7 
5-4 


gr< 













Differences .... 


1-9 


* 

+ 0-9 
.. 


+ 0-3 


+ 



X. 



grammes 

20-9 
19-7 



1-2 



Experiment 1338. Fired in explosion vessel Q, 70-99 grammes of Rottweil R. R. Density of charge 0-222. 
Pressure 16-47 tons per sq. inch (2510-6 atmospheres). 
Permanent gases 53,898-2 cub. centims. at C. and 760 millims. 
Aqueous vapour 11,576-7 cub. centims. at 0' C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


II. 


X. 


Found by analysis .... 
Originally in R. R 


grammes 
19-22 
19-82 


grammes 

41-76 
40 55 


grammes 

2-46 
o . 05 


grammes 

9-06 
x .in 


Differences .... 


- 0-GO 


+ 1-21 


+ 0-21 


+ 0-66 



Experiment 1337. Fired in explosion vessel Q, 92-74 grammes of Rottweil R. R. Density of charge 0-29. 
Pressure 21-5 tons per sq. inch (327 7 -4 atmospheres). 
Permanent gases 68,427 -3 cub. centims. at C. and 760 millims. 
Aqueous vapour 13,972'6 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


o. 


H. 


X. 


Found by analysis .... 
Originally in R. R 

Differences .... 


grammes 
25-55 

26-24 


grammes 

54-12 
53-68 


grammes 

3-19 
2-97 


grammes 

11-54 
11-10 


- 0-69 


+ 0-44 


+ 0-22 


+ 0-44 



2 H 2 



236 



SIR ANDREW NOBLE: EESEARCHES ON EXPLOSIVES. 



Experiment 1346. Fired in explosion vessel Q, 95'94 grammes of Rottweil R. R. Density of 
charge 0'30. 

Pressure 20-54 tons per sq. inch (3131'0 atmospheres). 
Permanent gases 70.802'3 cub. centims. at C. and 760 millims. 
Aqueous vapour 13,834-3 cub. centims. at C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


H. 


N. 


Found by analysis .... 
Ori^inallv in R R . 


grammes 

26-43 

27-16 


grammes 

56-14 
56-16 


grammes 

3-32 
3-07 


grammes 
12-00 
11-50 












Differences .... 


- 0-73 


- 0-02 


+ 0-25 


+ 0-50 



Esperime-nt 1401. Fired in explosion vessel Q, 127-92 grammes of Rottweil R. R. Density of 
charge 0-40. 

Pressure 34'9 tons per sq. inch (5320-0 atmospheres). 

Permanent gases 88,689'0 cub. centims. at 0" C. and 760 millims. 

Aqueous vapour 18,946'! cub. centims. at 0" C. and 760 millims. 

RECONCILIATION. 





C. 


0. 


H. 


N. 




grammes 


grammes 


grammes 


grammes 


Found by analysis .... 
Originally in R. R 


34-57 

35-85 


74-62 
73-33 


4-38 
4-06 


14-83 
15-16 


Differences .... 


1-2S 


+ 1-29 


4-0-32 


- 0-33 



Experiment 1402. Fired in explosion vessel R, 144-54 grammes of Rottweil R. R. Density of 
charge 0'45. 

Pressure 40-5 tons per sq. inch (6173-6 atmospheres). 
Permanent gases 98,819'4 cub. eentims. at C. and 760 millims. 
Aqueous vapour 19,568-1 cub. centims. at 0' C. and 760 millims. 

RECOXCILATIOX. 





C. 


0. 


H. 


N. 


Found by analysis .... 
Originally in R. R 


grammes 

39-29 
40-27 


grammes 
83-47 
82-38 


grammes 

4-86 
4-56 


grammes 
16-61 
17-03 












Differences .... 


- 0-98 


4- 1-09 


+ 0-30 


- 0-42 



[ 237 ] 



VII. Colours in Metal Glasses, in Metallic Films, and in Metallic 

Solutions. //. 

By J. C. MAXWELL GARNETT. 
Communicated by Professor L ARMOR, Sec.R.S. 

Received May 15, Read June 8, 1905. 
CONTENTS. 

Pages 

1. Introduction 237-239 

2. Expressions for the optical constants of media containing metal in amorphous or 

granular forms 239-242 

3. Formulae applicable only when the volume proportion of metal is small 242-243- 

4. Calculated numerical value of the optical constants of metal glasses, &c 243-248 

5. Diffusions of gold. The nature and form of the suspended particles 248-255 

6. Diffusions of silver. The nature and form of the suspended particles 255-259 

7. Blue reflection from the stained face of silver glass 259-263 

8. Diffusions of copper. The nature and form of the suspended particles 263-265 

9. Colouring effects of the radiation from radium, cathode rays, c 265-2G7 

10. Numerical values of the optical constants of media containing large volume proportions 

of certain metals 267-276 

11. Colour changes caused by heating metal films 277-282 

12. The exceptional case of beaten metal leaf 282-283 

13. CAREY LEA'S "allotropic" silver 283-285 

14. HERMANN VOGEL'S silver 285-286 

15. Allotropic forms of metal 286-288 

1. Introduction. 

THIS paper is an extension of a previous memoir on the " Colours in Metal Glasses 
and in Metallic Films "* ; it is concerned with the application of mathematical analysis, 
akin to that already there developed, to the explanation and coordination of the 
colours which certain metals are, under a great variety of circumstances, capable of 
causing. 

* 'Phil. Trans.,' A, 1904, vol. 203, pp. 385-420. 
VOL. CCV. A 393. 11.10.05 



238 ME. J. C. MAXWELL GARNETT 

From observations on gold and copper ruby glasses, it has been shown* that the 
first stage in the formation of a crystal of those metals is the small sphere ; and from 
observations on the growth of sulphur crystals in CS 2 , VoGELSANGt arrived at the 
conclusion that the small sphere is always the first stage in the formation of a crystal. 
He remarked, however, that it is by no means necessary that each of the small 
spheres, formed as crystallisation commences, should give rise to a separate crystal : 
the small spheres tend to coagulate; forming first rows and then groups of other and 
more complicated shapes, until the crystal is ultimately formed. To the intermediate 
bodies he gives the name of crystallites. 

That the spherical form of the nascent crystal is governed by surface tension, was 
suggested in the former paper.;}; If this suggestion is correct, we should expect that 
when the conditions are not the same in all directions, the spherical form of the 
nascent crystal will be replaced by an ellipsoidal form. In particular, when a very 
thin film of amorphous metal is heated until the molecules are sufficiently free to 
allow crystallisation to commence, the nascent crystals may be expected to be 
spheroids of the planetary type, having their axes normal to the film. Mr. G. T. 
BKILBY has observed such spheroids in thin films of gold and silver. 

Now it will appear below that metals are not only dichroic, exhibiting one colour 
by reflected light and, in thin films, another by transmitted light ; but that one and the 
same metal may, as its physical condition is altered, show a great variety of colours by 
reflected light, and a corresponding other series of tints by transmitted light. The 
ultimate cause of all these colours is to be found in the structure of the molecule itself. 
Juxtaposition, however, causes one molecule to afl'ect the vibrations of another. 
Thus consider a substance composed of molecules of a given metal separated from 
each other by the oether or by any other non-absorbing medium :|| the " effective free 
period " of the molecule of such a substance is dependent on the geometrical arrange- 
ment and density of distribution of the molecules in question. The optical properties 
of the substance will therefore depend on its microstructure. The object of this 
paper is to obtain information concerning the ultramicroscopic structure of various 
metal glasses, colloidal solutions, and metallic films, by calculating optical properties 
corresponding to certain assumed microstructures, and by comparing the calculated 
properties with those observed. 

* Lot:, cit. (pp. 388-392). When writing the former paper here cited I was unaware of VOGELSANG'S 
work. 

t H. VOGELSANG, "Sur les Cristallites," 'Archives Neerlandaises,' V. (1870), p, 156; VI. (1871), p. 223; 
VII. (1872), pp. 38-385. 

J Loc. cit., p. 392. The further suggestion there made that iu the colourless gold glass there are the 
molecules of gold present is, as will appear below, p. 251, erroneous. It is almost certain that in the 
colourless glass a gold salt is in solution, so that the heating has first to reduce the gold and then to allow 
the isolated molecules to run together into spheres. 

'Hurter Memorial Lecture,' Glasgow, 1903, p. 46. 

il As, for example, glass in a metal glass, or water in a colloidal solution. 



ON COLOURS IN METAL GLASSES, ETC. 239 

The microstructures to be assumed are suggested by the preceding remarks cm 
crystallisation. Calculations will be made for three types of microstructure, namely, 

(1) amorphous that in which the metal molecules are distributed at random ; 

(2) granular that in which the metal molecules are arranged in spherical groups ; 

(3) spicular* that in which these small spheres are replaced by oblate spheroids. 
It will subsequently appear that when the surrounding non-absorbing medium is of 
refractive index unity, an amorphous and a granular microstructure produce the same 
colours. 

In order to calculate the optical constants the refractive index and the coefficient 
of absorption which correspond to any given microstructure, it is necessary to know 
the values of the constants for some standard amorphous state of the metal. Now 
BEILBY t has shown that the process of polishing a metal surface causes the surface 
layer to " flow " as a liquid, and thus the polished surface is that of the metal in the 
amorphous state. It follows that the optical constants which we are to use as 
data for our calculations should, so far as possible, be those which have been 
determined by means of reflection from the polished surface of the metal in its 
normal state according to DRUDE'SJ method, rather than those obtained by means of 
the light transmitted through thin prisms of the metal, after the method adopted by 
KUNDT. 

2. Expressions for Optical Constants of Media containing Metal in Amorphous or 

Granular Forms. 

The optical properties of a homogeneous isotropic medium are determined when 
the values of the refractive index n and the absorption coefficient x, which correspond 
to light of every frequency, are known. We proceed to obtain the values of n and HK 
for a substance composed of molecules of metal embedded in an isotropic non-absorbing 
medium, the microstructure being amorphous. 

Consider then a medium consisting of one substance A, in solution in another C, so 
that the molecules of each substance are distributed at random. Let the number of 
molecules present per unit volume in the standard amorphous forms of A and C be 
respectively 9tf A and 9R C , and let the number of molecules present per unit volume of 
the composite medium be MA^A an d /AC^C respectively. We shall assume /A A and p. c to 
be constant throughout the medium ; or, more precisely, we assume that a length ?, 
very small compared with a wave-length of light, can be found such that, for all 
values of r greater than r , the number of molecules of A contained by a spherical 
surface situated wholly within the medium having a radius r and its centre being 

* The calculations for a spicular microstructure are reserved for subsequent publication, see note p. 241. 
t Loc. cit., Lord KAYLEIGH (Royal Institution Lecture on Polish, March, 1901) also holds the view that 
the process of polishing is a molecular one. 
J 'Ann. der Phys.,' XXXIX. (1889). 



240 MR. J. C. MAXWELL GAENETT 

situated at any point, is independent of the position of that point; thus f w/i^S^r*' 
depends only on r : and similarly for C. 

Suppose that when electromagnetic waves traverse this medium, the moments of" 
the average molecule of A and C in the vicinity of the point (x, y, z) are 

f A (*) = (/* A, A) and f c (t) = (f Cl ,f c ,fc). 

Then f A and f c are both proportional to E', the electric force exciting the average 

molecule* ; thus 

f* = 0,vE', f c = #cE'. 

The polarisation f ' (t) of the compound medium is given by 



Writing now E for E in the general equation t 

E' = E +tnf', 

we obtain 

E' = 
so that 

ft ( f \ _ 

' 
But MAXWELL'S equations for the composite medium are 



. df'ft) clE , cZH , ,, 

4?r ji-i + r = c curl H, - = c curl E, 
dt dt dt 

where c is the velocity of light in racuo. These may be written 

N' 2 j- = c curl H, ^-=- = c curl E, 
dt dt 

when we put 

If now we write 

N 7 = 'fl iu-'\ (9\ 

r\ /t \ L iK ) \^j- 

then n' and /c' are the refractive index and absorption coefficient of the composite 
medium. 

But the same analysis will show that if N A = n A (l IK A ) and N c = n c (l-iK c ) ; , 
where W A> K A and n c , K C are the optical constants of A and of C, then 

h and 



* Of. 'Phil. Trans.,' A, vol. 203, pp. 392, 393. 
t Loe. cit., equation (9), p. 393. 



ON COLOURS IN METAL GLASSES, ETC. 241 

Substituting these expressions in equation (I) we obtain 

N /2 -l N A 2 -1 N c a -l 
N' 2 +2 ~ MA N A 2 +2 +Mc N c 2 +2 ' 

If, now, we suppose that C is a transparent isotropic substance of refractive index v, 
and that A is a metal, we have, by omitting the suffix A and putting /u, c = 1 ft, 

N /2 -l N 2 -l , .v 2 -! 
N' 2 +2 /A N 2 +2 +( M V+2' 
or, 

22 , 



N' 3 +2 
When fj, is very small this equation becomes 

......... (4). 



These equations give the optical constants of the metalliferous medium in the 
amorphous state. When the microstructure is granular, these equations (3) and (4) 
are, as has been already shown,* replaced by 

N' 2 -V = _N 2 -v 2 /r , 

N' 2 +2v 2 I 
so that when p. is small, 



Comparison of equations (3) and (5) shows that the optical properties of a 
metalliferous medium, containing a given volume proportion ju, of the metal, vary 
according as the metal is in small spheres or in a state of molecular subdivision, 
except when //,= !. Thus when metal is in solution in water or glass the colour of 
the compound medium will change as crystallisation commences. When, however, 
v = 1, the equations (3) and (5) both reduce to 

N' 2 -l N 2 -l m 

N /2 +2 ^N 2 +2 ' 

It follows that the optical properties of a metal in a state in which its specific 

* Loc. tit., equations (11) and (12), p. 394. The mathematical treatment of the optical properties of 
media containing minute metallic ellipsoids, instead of the spheres which give the granular microstructure, 
is under consideration, but, with the exception of the case wherein the volume proportion, p., of metal is 
small, it is not yet complete. 

[Note added 1st August, 1905. The investigation of the general case (any value of /*) has now been 
completed. The results for the case when p. is small, which, when this memoir was communicated to the 
Royal Society, were given in 12, have therefore been reserved for subsequent publication in a more 
complete form.] 

VOL. COV. A. 2 I 



242 ME. J. C. MAXWELL GARNETT 

gravity has any known value, are unaltered by a change in the raicrostructure from 
amorphous to granular.* Or, again, Professor R. W. WOOD'S clouds of sodium 
vapour, t for which v = I nearly, do not change colour as condensation commences. 

3. Formula? Applicable only when the Volume Proportion of Metal is Small. 

The volume proportion of metal present in all the coloured glasses and colloidal 
solutions which we shall discuss below is small. We proceed to obtain, from 
equations (4) and (6) above, expressions for the optical constants of media, such as 
glass or water, holding in suspension metal in the amorphous and granular states. 

Let N" EE n" (I LK") denote the optical constants of the compound medium when 
the metal is in the amorphous state in true solution. Then, replacing N' by N" in 
equation (4), we have 

2 say. 



Equating real and imaginary parts, we find that 

, ^(l-*" 2 )-^ K(K 2 +l)} 2 +ft 2 (* 2 -l)(v 2 -2)-2v 2 

2 --* 



(2 + j/V " K(/c 2 -l)-2} 2 +4nV J 

From (8) we have 

n" 2 ( 1 - K " 2 ) = S + (2 + v 2 ) pa', n"* K " = (2 + v 2 ) /*', 
so that, neglecting ju, 2 , we obtain 

wV = (2 + !/)/?. ^ n" = v {l + (2 + v 2 )/2v 2 . l j M '} .... (9). 



The corresponding values of W = n'(l iK f ), the optical constants when the 
metal is in the granular state, have already been obtained.! They are reproduced 
here for convenience of reference : thus 



n' K ' = 3fjL V /3, w' = v(l+|./4) ....... (10), 

where 



a = 



, , 



* For example, the tables given in the previous paper ('Phil. Trans.,' A, 1904, p. 406), and the curves 
shown (loc. cit., pp. 411-414), as well as the tables and curves given in 10 of the present communication, 
represent optical properties of the media as /* diminishes from unity to zero, whether that diminution is 
associated with the formation of small spheres or whether the metal retains its amorphous state throughout 
the change in /. 

t Brit. Assoc., Cambridge, 1904. 

t Loc. cit., 5, pp. 394, 395. 



ON COLOURS IN METAL GLASSES, ETC. 243 

Thus, when light of wave-length X traverses a thickness d of a metalliferous 

n"n" n'n' 

medium, the intensity of the light is reduced in the proportion* e~ M A or e~ M * 
according as the metal is in true solution or in spherical aggregates. 

Suppose now that two kinds of monochromatic light, of wave-lengths Xj and X 2 , are, 
by traversing a distance d in an absorbing medium, reduced in intensity by e~ K<d and 
e -:M res p ec tively. Then the absorbing medium reduces the proportion of the inten- 
sities of the two kinds of light in the ratio e~ (Kl ~ v>d , which is a function of d. Thus 
the tint of a coloured medium, viewed by transmitted light, depends on its thickness.! 
We shall, however, speak of two absorbing media as possessing the same colour when, 
whatever be the values of X x and X 2 , the ratio KI : K 2 is the same for either medium ; 
for, if suitable thicknesses of such media be chosen, the light transmitted by them will 
be of precisely the same tint. 

Since, therefore, it appears from equations (8) and (9) above that the ratio 



is independent of v, it follows that a niolecularly subdivided metal produces the same 
coloration (by transmitted light) in all non-dispersive transparent isotropic " solvents," 
irrespective of their refractive indices. \ Thus, neglecting the small dispersion, a 
borax bead and a glass bead, each containing a metal in solution, will be of the same 
colour ; but so soon as crystallisation of the metal begins, so that part of the metal is 
in small spheres, the beads will cease to be of the same colour, since the ratio 



is not independent of v. 

4. Numerical Values of Optical Constants of Metal Glasses, &c. 

Consider any transparent isotropic non-dispersive medium of refractive index v, 
containing either molecules or small spheres of a metal, the optical constants of 
which, for light of wave-length X, are n and UK, the particles of metal being so 
distributed that there are many of them to a wave-length of light. The 
"absorptions," nV/X and w'V/X, of the compound medium can be easily determined 
by means of equations (9) and (10), when the values of a, ft, a!, /3', are known for 
light of wave-length X. These values can be calculated by means of equations (11) 

* Of. 'Phil. Trans.,' A, 1904, p. 395. 

t Thus, for example, a thin sheet of gold ruby glass will appear pink, a considerable amount of blue 
light being transmitted, whereas a thick sheet of the same glass will appear deep red, almost like a copper 
ruby. Again, by increasing the depth of a silver stain on glass, we get all gradations in colour from 
canary yellow through amber to red. 

| This, then, must be the colour of the vapour of the metal provided that the molecules are monatomic, 
or, at least, do not dissociate when the metal is vapourised. We shall term it the " vapour colour." 

2 I 2 



244 MR. J. C. MAXWELL GARNETT 

and (8), when the quantities n and UK have been determined for the light in question 
by direct experiment on the metal in the standard amorphous state. R. S. MINOR* 
has made such experimental determinations, for various kinds of monochromatic light, 
from the polished surfaces of silver and copper. His values of n and n/c for silver 
and copper, together with the numerical values of a, ft, a!, ft', and of certain other 
functions as calculated for various values of v, are shown in Tables II. and III. The 
values of n and n/c, for X = '630 and X = '589 only, have also been determined by 
DRUDEf from the polished surface of gold ; but values of n and HK for other values of 
X have been obtained by HAGEN and RUBENS J from gold prisms deposited on glass. 
Since however the state of the metal in the prisms is not known, these latter values 
cannot be depended upon for our purpose ; but as a rough estimate of the values of 
a, ft, a', ft', &c., may be formed by their means, the numerical values of these quantities 
have been calculated ; the results are shown, together with all the observed values of 
n and UK, in Table I. The wave-length X of the light will throughout be measured 
in thousandths of a millimetre. 

All the calculated numbers given in Tables I., II., and III. have been carefully 
checked with a " Brunsviga " machine. I believe that in no case does an error 
amounting to 1 per cent, survive in these Tables, which must accordingly supersede 
those -given in the former communication. || 



* R. S. MINOR, 'Ann. der Phys.,' vol. X., 1903. 

t 'P. DRUDE, 'Physik. Zeitschr.,' January, 1900. 

\ RUBENS, ' Wied. Ann.,' vol. XXXVIL, 1889. 

It will appear in the sequel that on this account the optical properties of silver glasses and of colloidal 
solutions of silver are much more accurately represented by our calculations than is the case with gold 
ruby glasses and colloidal solutions of gold. 

|| Lot. tit., p. 396. 



ON COLOURS TN METAL GLASSES, ETC. 



245 



TABLE I. Gold. 



X 




. { 


6562 


6300 


5892 


5269 


4584 
/F + QX 






I 


(C). 




(D). 


(E). 


( 2 / 


UK 






2-91* 


3-15t 


2-82t 


1-86* 


1-52* 


















n 






38* 


31f 


37f 


53* 


79* 






















a. 


2-50 


2-27 


2-65 


83 


46 






ft 


479 


251 


584 


1-068 


552 






a? + p 








C ft . 1 Q 


00 . J 


Glass \ 
v = 1-56 / ' 




A 4 


38 Go 


o4 44 


oy o< 










ri'ic" (v* + 2)P 
















H*A. vX 


47 


oU 


Oo 










M'K' 3^ 

TX x~ 


3-42 


1-86 


4-64 


9-49 


5-63 


Glass \ 
v = 1-5J- ' 




V 3vj8 

7U ~ "T 


2-33 


1-30 


3-12 


8-97 


5-17 


Water at 19 C.\ 
v= 1-3333 J 




UK 3vft 
~jl\ T 


1-293 


766 


1-687 


9-906 


6-034 


Vacuum v = 1 "1 
(Vapour colour) J 




TI'K' 3/2 

TA ~ : T 


338 


214 


417 


3-191 


4-019 



RUBENS. 



t DRUDE. 



246 



MR. J. C. MAXWELL QARNETT 



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ON COLOURS IN METAL GLASSES, ETC. 



247 



TABLE III. Copper. 



X 


. . . 


3467 


395 


450 


500 


535 


550 


575 


5892 


630 


UK 


. . . 


1-466 


1-763 


2-149 


2-341 


2-276 


2-233 


2-428 


2-630 


3-012 


n 




1-190 


1-173 


1-131 


1-098 


1-004 


892 


651 


617 


562 




ft 


435 


560 


683 


701 


781 


891 


1-114 


890 


465 


Glass ~1 


H"K" 


4. AO 


3. OOQ 


O M*7 


2. AKA 


*) . 1 AO 


o . f)f\Q 


1 f>71 


1 1 1 f\ 


. KQQ 


i/ = 1-56 / ' ' 


/.A 






















mV 

TX 


5-875 


6-661 


7-107 


6-559 


6-829 


7-579 


9-279 


7-065 


3-453 


Glass \ 
v = 1-5J 


wV 

TX 


5-797 


6-420 


6 568 


5-897 


6-180 


6-890 


7 634 


5-699 


2-759 


Vacuum v = 1 "1 
(Vapour colour) J 


T>'K' 

7IT 


1-104 


921 


642 


492 


504 


530 


404 


268 


142 



We have now to compare the observed optical properties of various media coloured 
by gold, silver, and copper with those corresponding properties which, according to 
the Tables I., II., and III., would be exhibited by the media if the colouring agent 
were the metal itself, in either the molecularly subdivided or the granular state. 

The simplest of the optical properties to observe and to measure is the absorption of 
light by the medium. Although the absorptions of colloidal solutions of various 
metals, and even of suspensions of metals in gelatine, have already been measured for 
several values of the wave-length, X, of light, no such measurements of the absorption 
of glasses coloured by metals appear to have yet been made.* Owing, however, to 
their permanence, such media seemed likely to yield the surest information as to the 
chemical and physical nature of their colouring agents. The absorptions of a series 
of glasses coloured with gold, silver, and copper have therefore been measured for me 
at the National Physical Laboratory, under the supervision of Mr. F. J. SELBY. The 
silver glasses consisted of a silver stain on one side of a colourless glass, the refractive 
index of which was, for sodium light, equal to v = 1'579. The gold ruby glasses 
were flashed on to colourless glass. Both the silver and gold glasses were, to 
ensure purity of materials, specially prepared at the Whitefriars Glass Works by 

* Except two gold glasses, the absorption curves for which are given by ZSIGMONDY ('LiEB. Ann.,' 
vol. 301, pp. 46-48). 



248 



MR. J. C. MAXWELL GARNETT 



Mr. H. J. POWELL, to whom I am much indebted for the trouble he has taken on 
my account. The copper ruby glass used was the ordinary commercial flashed glass. 
The absorptions of the various glasses are indicated by the curves marked Au (A) 
and Au (B) in fig. 2, Ag (B) in fig. 4, and Cu (X) in fig. 7 ; the ordinates representing 
the quantity K, where e~ K represents the proportion of light of wave-length X, 
transmitted by the glass after allowance has been made for reflections, and the 
abscissae representing the corresponding values of X. The scales on which Au (A) and 
Au (B) are represented are such that K has the same value for both at the D line 

(X = -589). 

The following are the values of K measured at the National Physical Laboratory 

for the respective glasses : 

TABLE IV. 



Glass 


Au(A). 


Au (B). 


Ag(B). 


Cu(X). 


X. 


K. 


K. 


X. 


K. 


X. 


K. 


698 




080 


696 





698 


300 


696 


113 





664 





664 


378 


664 


154 


140 


606 


063 


634 


563 


606 


324 


406 


562 


112 


606 


1-038 


562 


878 


1-532 


528 


210 


584 


2-496 


553 


1-400 


2-175 


500 


384 


573 


3-309 


544 


1-990 3-0065 


478 


809 


567 


3-484 


537 


2-487 


3-7485 


458 


1-363 


562 


3-484 


528 


2-551 


4-050 


442 


2-514 


544 


3-091 


514 


2-122 


3-224 


436 


2-894 


528 


2-952 


500 


1-495 


2-344 


429 


3-003 


514 


2-985 


478 


1-030 


1-628 


422 


2-225 


500 


3-023 


458 


954 


1-456 


406 


1-520 


478 


3-270 


442 


981 











458 


3-484 

















441 


3-789 

















436 


3-807 



5. Diffusions of Gold. TJie Nature and Form of the Suspended Particles. 

The present section will be concerned with the colours produced by diffused 
particles of gold. The values of the expression nV//A for v = 1'5, v = 1'3333, and 
v = 1 given in Table I. are plotted in fig. 1. The curves shown in that figure have 
been drawn to pass through the plotted points, the coordinates of the maximum for 
each curve being determined by assuming n and n/c to vary continuously for values 
of X intermediate between the abscissae of the plotted points on either side of those 
maxima. According to the remarks in the preceding section, these curves must not 
be regarded as accurately representing the absorption of gold spheres in glass, of 
gold spheres in water, and of gold vapour (or gold spheres in vacuo) respectively ; 
they should, however, enable us to form a fair estimate of the absorption in question.* 

* See footnote , p. 244. 



ON COLOURS IN METAL GLASSES, ETC. 



249 



Fig. 1. GOLD calculated values of -^- . 

A 



Fig. 2. GOLD. 
(1) K, observed fov gold ruby glass Au(A) : 

(1) Spheres (or molecules) in vae.uo, v= 1 : (3) K, observed for gold ruby glass Au(B): - 

(2) Spheres in water at 19 C., v= 1-3333: - Observed values : . 

(3) Spheres in glass, v = 1 5 : 



Calculated values are shown thus : 0. 



(3) _, calculated for gold spheres in 

A 

glass, v 1 5 : 

Calculated values : x . 




VOL. CCV. A. 



2 K 



250 MR. J. C. MAXWELL GARNETT 

In fig. 2 the graph of nY/X for glass (v = I'd), shown by a broken line in fig. 1, is 
again represented ; but here on such a scale as to have the same ordinate at X = '589 
as that of the graphs of the observed absorptions of Au (A) and Au (B). The 
calculated and observed curves resemble one another in having a minimum in the red 
and a maximum in the green, although the calculated maximum occurs at about 
X = '550, while the observed maximum falls at X "= '533. Also both calculated and 
observed absorptions fall from green to blue, while the dotted curve in fig. 1 shows 
that the absorptions produced by molecularly divided gold will increase from green 
to blue, having a maximum at about X = '475. These results then, so far as they go, 
are in accordance with the suggestion, put forward in the former memoir, that 
the colouring agent of gold ruby glass consists primarily of diffused spheres of gold, 
although some discrete molecules may also be present. The following is the evidence 
which has accumulated to show that a gold ruby glass contains minute spheres ot 
gold, many to a wave-length of light, and that it is to these small gold spheres that 
the pink colour of the glass is primarily due : - 

(1) There are particles, presumably of gold, visible in all specimens of gold ruby glass in which the 

colour has been developed.* 

(2) Whenever these particles are of diameter less than 10~ 5 centim. they are spherical in shape.t 

(3) SIEDENTOPF and ZSIGMONDY statej : " It is only in the case of ruby glasses that the particles are 

so dense that they cannot be fully separated under the microscope." In other words, whenever 
there are many small spheres to a wave-length of light, the glass is ruby. 

(4) We have just seen that, within the limits of experimental error, this ruby colour is that which 

would be produced by small spheres (but not by molecules) of gold, many to a wave-length, 
embedded in the glass. 

(5) The polarisation of the cone of light emitted by the particles in the path of a beam of white light 

traversing any of the three ruby glasses examined by SIEDENTOPF and ZsiGMONDY is that 
which would be possessed by the cone of light emitted by small spheres of metal embedded in 
the glass. Further, the colour of the cone of light in the case of these three glasses was green, 
while it has been shown in the former paper|| that the intensity of light of wave-length X 
emitted by small spheres of gold embedded in the glass is proportional to (a 2 + 4y8 a )/X 4 , and, 
according to Table I. above, this expression for gold spheres in a glass of refractive index 
v = 1 -56 has a maximum in the neighbourhood of X = -560, i.e., in the yellowish-green. 

We conclude then that the colouring agent of gold ruby glass is metallic gold,! the 
major portion of which is in the form of small spheres. 

The irregular blue and purple which often appear, instead of the ruby at which the 
glass manufacturer aims, can be explained as indicated in the appendix to the former 

* SIEDENTOPF and ZSIGMONDY, ' Ann. der Phys.,' January, 1903. 
t Cf. former paper, 'Phil. Trans.,' A, 1904, p. 391. 
I Loc. tit., p. 27. 

See their table reproduced at p. 397 of the former paper and discussion following it on pp. 398-401 
('Phil. Trans.,' A, 1904). 
|| Loc. cit., p. 400. 
U Not aurous oxide, as stated in the text-books on glass making. 



ON COLOURS IN METAL GLASSES, ETC. 251 

paper. We have already* seen that if gold glass when first made in the furnace be 
rapidly cooled, the glass remains colourless. In order to obtain ruby glass, the molten 
glass must be left in the annealing oven and maintained at a high temperature for 
about three days. If the glass is too violently heated or is kept too long at a high 
temperature, it becomes turbid, reflects brown light, and develops first an amethystine 
and then a blue tint by transmitted light. But it now appears that the gold cannot, 
as previouslyt suggested, be in solution in the colourless glass when first heated ; for 
if metallic gold were in true solution in the glass it would have the vapour colour 
indicated by the dotted curve in fig. 1. The gold must therefore be gradually reduced 
during the annealing process. So long as the glass remains hot enough to admit of 
molecular movement, the molecules of gold go together to form spheres, and these 
small spheres tend to coagulate into crystallites.} If the glass cools before the 
coagulation of the small spheres, a gold ruby glass is obtained. If, however, some of 
the small spheres have coagulated into crystallites, the density of which exceeds '6 
of that of normal gold, these crystallites will reflect light which is predominantly 
yellow or red.|| The glass will thus reflect brownish light; and since the more 
refrangible rays are less reflected than those of longer wave-length, the red end of the 
absorption curve will, owing to the crystallites, be raised relative to the blue. The 
glass will thus appear bluer than when no coagulation has occurred. Further, as 
these crystallites may be of dimensions comparable with a wave-length of light, they 
destroy the optical continuity of the medium and produce turbidity. Now the blue 
colour of a gold glass is always associated with turbidity and a brown appearance by 
reflected light, so that the formation of crystallites of gold in the glass accounts for 
the irregular blue and purple colours which gold glass sometimes exhibits. 1 

Diffusions of gold particles in water the so-called "colloidal solutions" of gold- 
have been prepared by FARADAY**, ZsiGMONDY,tt and STOEKL and VANINO^, who 

* Loc. cit., p. 392. 

t Loc. cit., p. 392. 

J In the case of copper ruby glasses the process continues until actual crystals of copper are formed, 
but I have not seen gold crystals in a glass, although it is probable that they are occasionally formed. 

KIRCHNER and ZSIGMONDY ('Ann. der Phys.,' XIII., 1904, p. 591) estimate that a clump of gold 
particles in a blue gold-gelatine preparation contains at least 50 per cent, of gold. See below, p. 254. 

|| See fig. 12, below. 

U The blue and violet [purple] colours of the glasses D and E in SIEDENTOPF and ZSIGMONDY'S table 
(see ' Phil. Trans.,' A, 1904, p. 397), as well as the red, yellow and brown colours of the cone of light 
emitted by them, are thus explained. STOKES (Royal Institution Lecture, 1864, 'Collected Works,' 
vol. IV., p. 244), without entering into the question why gold glass ordinarily transmits pink light, says 
that, it being the property of gold to transmit bluish light, the metallic gold in suspension causes the blue 
appearance. 

** FARADAY, Bakerian Lecture for 1857, printed in 'Phil. Trans.' for 1857, and reprinted in his 
'Researches in Chemistry and Physics.' References will be made to the pages of the reprint. 

ft ZSIGMONDY, 'LiEB. Ann.,' vol. 301 (1898), p. 29, and 'Zeitschr. f. Electrochem.,' vol. IV., p. 546. 

II STOEKL and VANIXO, 'Zeitschr. f. Phys. Chem.,' XXX. (1899), p. 98. 

2 K 2 



252 ME. J. C. MAXWELL GAENETT 

precipitated the gold from its chloride by means of various reducing agents ; and by 
BREUIG* and later by EHRENHAFT, t who used a gold terminal for an electric arc 
which was caused to spark under water. 

All these preparations exhibited a gradual change in colour from red through purple 
to blue ; this change was greatly accelerated by the introduction of a trace of salt 
into the water. ZSIGMONDY^ gives the absorption curves of a number of "solutions" 
of gold. STOEKL and VANINO measured the absorptions of a red suspension con- 
taining a known volume proportion of gold. Lastly, EHUENHAFT|| has made careful 
measurements of the absorptions of "colloidal" gold. The curves plotted from his 
measurements of the red "solutions" resemble the continuous curve shown in fig. 1. 
Again, EHRENHAFT statesll that the absorption band of a gold suspension which 
possessed a beautiful red colour began at X = "560 and attained a maximum at 
X = -520, while the solution was almost transparent in the ultra-violet. Now the 
maximum of the calculated absorption curve for spheres of gold in water (v = 1/3333) 
occurs at X = '533.** Again, the dotted curve in fig. 1, which will represent the 
absorption produced by a true solution of gold, does not sufficiently agree with the 
measured absorptions to admit of the gold being in true solution in the water. These 
results suggest that the coloration is due to diffused spheres ft of gold, although some 
discrete gold molecules may also be present. 

* BHKDIG, ' Zeitschr. f. Phys. Ghcm.,' XXXIL, p. 127. 

t F. EHREXHAFT, 'Ann. der Phys.,' XI. (1903), p. 489. 

{ ZSIGMONDY, 'LiKP,. Ann.,' vol. 301 (1898), pp. 46-48. 

Loc,. cit., p. 108. For a discussion of their rusults see below (footnote, p. 253). 

|[ Loc. fit., pp. 505, 506. 

H Of., table given, lor. fit., p. 507. 

** Thus the differences in wave-length between the observed maximum absorption of gold ruby glass and 
of the calculated maximum for gold spheres in glass (;' = 1'5), and between the observed maximum for 
colloidal gold and the calculated maximum for gold spheres in water, are respectively '017 and "013, and 
these differences are of the same si/.e. 

ft EHREXHAFT also supposed that the gold was present in the form of small spheres ; but he proceeded 
to define the average size of these spheres (and also of those of Ag, Pt, &c., in the " colloidal" solutions of 
these metals) by means of J. J. THOMSON'S equation connecting the radius of a conducting sphere with 
the wave-length corresponding to the free periods of its vibration, this wave-length being assumed to be 
that of the absorption maximum. KIRCHXER and ZSIGMOXDY (' Ann. der Phys.,' 1904, p. 575), however, 
point out that there is no connection between size of particles and the absorption of light produced by 
them, and this we have seen to be the case, provided there are many particles to a wave-length ; also the 
very small size (if spherical, their average diameters would be 7///J.) of the particles of gold, the gold content 
of which ZsiGMONDY measured would require the absorption maximum to be in the ultra-violet. 
KlRCHXER and ZsiGMOXDY add that it would only be possible to get a large enough linear dimension to 
give a free period if the particles were not iso-dimensional, and they conclude therefore that the gold 
particles must be in the form of leaves or of rods ; but they do not reconcile such a form with the 
polarisation and green colour of the cone of light emitted by the smaller particles. Since, however, we 
find that the small-sphere hypothesis accounts for the observed phenomena, we must agree with 
EHREXHAFT that the particles are spherical, although we cannot admit that the average diameter of the 
spheres is correlated to the wave-length of the light most absorbed. 



ON COLOURS IN METAL GLASSES, ETC. 253 

This view enables us to explain the change of colour from red to blue, by the 
coagulation of the small spheres, just as in the case of the glasses coloured by gold ; 
the simultaneous development of a brown reflection and a turbid appearance is at 
the same time explained. The following quotations must suffice to describe the 
phenomena in question. 

FABADAY observes that 

"A gradual change goes on amongst the particles diffused through these fluids, especially in the cases 
where the gold is apparently abundant. It appears to consist of an aggregation. Fluids at first clear, or 
almost clear, to ordinary observation, become turbid; being left to stand for a few days, a deposit falls."* 

When common salt, or any other substance which dissociates in water, was added 
to the fluid 

"... The salt diffused gradually through the whole, first turning the gold it came in contact with 
blue, and then causing its precipitation.! 

" Such results would seem to show that this blue gold is aggregated gold, is., gold in larger particles 
than before."} 

Again 

" The supernatant fluid in specimens that had stood long and deposited was always ruby . . . there 
was every reason to believe that the gold was there in separate particles, and that such specimens afforded 
cases of extreme division." 

Observations made by subsequent physicists agree with those of FARADAY. Thus 
ZSIGMONDY writes 

" In every case the bright red colour [of suspensions of gold in water] changed to blue on the addition 
of salt; and decoloration of the upper part of the liquid showed that precipitation has then begun."]] 

Again, STOEKL and VANINO, who examined a large number of suspensions of gold 
in water prepared by many different methods, state that 

" When the particles [of gold] are very small ... the fluid appears red-yellow, ruby-red. When, 
however, the particles increase in size, the red and yellow rays are quite cut off and the transmitted light 
consists only of blue and violet rays, the fluid appearing blue-violet. "U 

* ' Researches in Physics and Chemistry,' p. 414. 

t We may suppose that by friction against the water the gold spheres obtain that negative change 
which ZSIGMONDY (' LIEB. Ann.,' vol. 301, p. 36) found that they possess. The mutual repulsion of these 
like charges prevents the spheres from coagulating and thus keeps the gold in suspension in the water. But 
when an electrolyte is introduced into the fluid, the positive ions discharge the gold spheres, so that 
coagulation and precipitation result. 

\ FARADAY, loc.. cit., p. 420. 

FARADAY, loc. cit., p. 418. 

|| ZSIGMONDY, ' LIEB. Ann.,' vol. 301 (1898), p. 34. 

II ' Zeitschr. f. Phys. Chem.,' XXX. (1899), p. 108. 

As already stated, STOEKL and VANINO measured the absorption of light, for six different values of \ 
by a suspension containing a known volume proportion of gold. Using their value of /x(- 000003) to 
determine the scale of the continuous curve in fig. 1, and comparing the values of wV/A so obtained with 



254 MR. J. C. MAXWELL GARNETT 

Finally, KIRCHNER and ZSIGMONDY record that in a gold suspension in water 

"... A given (generally large) number of particles which diffract green light [i.e., small spheres] were 
brought together by the addition of an electrolyte into a single particle which diffracted yellow or red 
light with much greater intensity* than its components. With this uniting of particles occurs the change 
in the colour of the fluid from red to blue."t 

We have already shown that, theoretically, the coagulation of the small spheres of 
gold should produce a colour change in the fluid, from red through purple to blue ; 
and the above quotations have indicated that coagulation accompanies the change of 
colour. But that the coagulation takes place in the manner assumed for the purposes 
of the theory has been shown by KIRCHNER and ZSIGMONDY, who prepared suspensions 
of gold in gelatine, some of which preparations were red when wet, and changed to 
blue on being dried, at the same time developing a gold-bronze reflection. J 

Now these dry blue membranes contained a number of clumps, each composed of 
hundreds of ultra-microscopic resonators^ (small spheres) ; and these clumps were 
comparable in size with a wave-length of light, being directly visible when examined 
with a numerical aperture of T4 : they would therefore be capable of reflecting light. 
Further, the change of colour to blue was most marked in those preparations in which 
the individual clumps were most dense, || and it appears from fig. 12 below that the 
selective absorption of red and yellow light by a gold crystallite is greater the greater 
its density. The theoretical explanation of the change to blue requires the rays of 
lower refrangibility to be stopped by reflections from crystallites,!! and this requirement 
is thus satisfied. 

the absorption curve obtained from STOEKL and VANINO'K observations, we find that the observed curve 
lies below the calculated curve, except for red light. But SroEKr, and VANINO record that the observed 
fluid had a yellowish reflection, so that large particles (crystallites) must have been present in it ; and the 
presence of these crystallites requires the volume // of gold, which per unit volume of the liquid is in the 
form of small spheres, to be less than the total volume proportion /x This diminishes the absorptions 
throughout the spectrum. But the volume proportion /*-/*' of crystallites produces absorption which is 
much greater for the red and yellow than for the green and blue rays. The superposition of the 
absorptions produced by /<,' and by //. - // would thus produce an absorption curve in accordance with that 
observed. 

^ The aggregate may be supposed to be comparable in size with a wave-length of light ; the intensity 
of the light reflected from it would thus be proportional to the square of its diameter, while the intensity 
of the light diffracted by the small spheres is proportional only to the sixth power of their diameters. 

t KIRCHNER and ZSIGMONDY, he. tit., p. 592. 

| Loc. cit., p. 589. 

KIRCHNER and ZSIGMONDY, loc. cit., p. 576. 

|| Loc. cit., p. 577. 

U A similar explanation possibly applies to the fact that when light, transmitted through a stretched 
membrane containing gold in suspension, is polarised in the direction of stretching, the emergent light is 
red, but when the incident light is polarised in a perpendicular direction the colour is blue, the gold 
clumps being comparable with a wave-length in the direction of stretching, but not in a perpendicular 
direction. (Of. AMBRONN, 'Ber. d. math.-phys. Kl. d. k. Sachs. Gesellsch. d. Wissensch.,' December 7, 1896, 
and AMBRONN and ZSIGMONDY, do., July 31, 1899). 



ON COLOUES IN METAL GLASSES, ETC. 255 

In conclusion, we remark that most " colloidal solutions" of gold, even those which 
are of a ruby colour, contain crystallites in addition to the small spheres to which the 
colour is primarily due. Thus FAKADAY could detect the green " cone of light," 
which indicates the absence of large aggregations, only in those liquids which had 
been cleared by prolonged precipitation and frequent decantation ; and STOEKL and 
VANINO found that all the gold suspensions which they examined showed a yellowish 
reflection. A small number of the large aggregations may, however, cause the cone 
of light to appear yellow or red without appreciably altering the colour of the 
transmitted light. For, whereas the intensity of the (green) light emitted by a small 
sphere is proportional to the sixth power of the diameter, the intensity of the (brown) 
light reflected from a gold crystallite is proportional to the square of its linear 
dimensions. Gold solutions prepared chemically appear, however, to be freer from 
aggregated gold than are those prepared by BRE DIG'S method.* 

6. Diffusions of Silver. TJie Nature and Form of the Suspended Particles. 

We proceed to consider the absorption of light produced by diffused particles of 
silver. The values of nY//nX for v = T6, v = 1 P 5, v = 1'3333, and v = I'O given in 
Table II. are plotted in fig. 3, the positions of the maximum of each curve being 
determined as in the case of gold. Since (cf. above, 4) the values of n and HK for 
silver were all determined from the polished surface of the metal, these curves should 
represent the absorption produced by diffused spheres of silver in glass, in water, and 
in vacua, with only a small error, t The dotted curve in fig. 1, which represents the 
absorptions of diffused molecules of silver in vacuo (and, on different scales, in other 
non-absorbing and non-dispersive media), shows that the silver molecule has a free 
period corresponding to X = "3GO, about. The existence of this free period is possibly 
responsible for the sensitiveness of silver salts to ultra-violet light. 

In fig. 4 the graphs of wV/X for glasses of refractive indices v = 1'GO and v 1'56 
are shown on such a scale as to have the same ordinate at the D line as the graph 
of K for the measured glass Ag (B), of which the measured refractive index at the 
D line was T579. The measured curve resembles those calculated, following them 
very closely from X = '600 to X = "475, and having a maximum for a value of X 
intermediate between those values of X which correspond to the maxima of the two 
calculated curves.^ This close approximation of the observed absorptions to those 

* Cf. ZSIGMONDY, ' Zeitschr. f. Electrochem.,' p. 547. BREDIG'S remark, that his gold solutions were blue 
red, points to the same conclusion. 

t These curves show that in each case the absorption is less for red than for yellow. This is contrary 
to statements made in the previous paper (loc. tit., pp. 399 and 420) ; the errors therein made were due to 
miscalculation for silver (red) (loc. cit., Table I., p. 396). 

J The cause of the depression of the observed maximum below those calculated is doubtless to be found 
in the fact, to which Lord RAY LEIGH has called attention in a recent lecture at the Royal Institution, that 



256 



MR. J. C. MAXWELL GARNETT 



IIK 



, Fig. 4. SILVER. 

Fig. 3. SILVER calculated values of . ,,! j * i A /D\ 

A. (1) K, observed for glass Ag (B) : 

Observed values : x . 



(1) Spheres (or molecules) in vacua, v=\-0: 

(2) Spheres in water. v=l- 3333 : 

(3) Spheres in glass, v = 1 5 : 

(4) Spheres in glass, v = \ 6 : 

Calculated values shown thus: O- 



(2) ^-, calculated for silver spheres in 

A 

glass, v = 1 56 : 

(3) - , calculated for silver spheres in 

A 

glass, v - \ ' GO : 

Calculated values : Q . 




ON COLOURS IN METAL GLASSES, ETC. 257 

calculated suggests that the colouring agent of the yellow silver glass consists primarily 
of diffused spheres of silver. Since discrete silver molecules would produce an 
absorption maximum at X = '360, not more than a comparatively small amount of 
silver can be present in the molecularly subdivided condition. The conclusion that 
silver glass owes its colour to diffused spheres of silver will be verified in the following 
section. 

The absorption spectra of some colloidal solutions of silver, prepared by BREDIG'S 
method,* have been measured by EHRENHAFT. The continuous curve shown in fig. 3, 
representing the calculated absorptions of a diffusion of silver spheres in water, is of 
the same form as that which, according to EHRENHAFT'S measurements, represents 
the absorption of visible light by a colloidal solution of silver.! Using ultra-violet 
light, he further found that a brown colloidal solution of silver, examined before 
coagulation had seriously affected its colour, showed an absorption band which began 
a,t X = '503 and attained a maximum at X = '380, while the fluid was again quite 
transparent at X = '335. Except for the fact that the maximum ordinate of the 
calculated curve for silver spheres in water is at X = '389 instead of at X = '380, the 
above observations admirably describe the continuous curve shown in fig. 3. Since 
the dotted curve given in that figure shows a maximum at X = '360, and the absorp- 
tion band does not begin until X = '450, about, the colour of the " colloidal " solution 
is not that which would be exhibited by a suspension of discrete silver molecules, i.e., 
by a true solution. We conclude, therefore, that the silver in a " colloidal " solution 
is present in the form of small spheres ; discrete molecules may, however, also be 
present, and, as indicated above in the case of gold, prepared by BREDIG'S method, 
probably also crystallites, the number and size of which will increase with the age of 
the solution. 

That the silver in a colloidal solution is in the form of small spheres is further 
shown by an experiment of BARUS and SCHNEIDER j who measured the refractive 
index of such a fluid. Their results are given in the following table, in which n 
represents the measured refractive index : 



the spectrum formed by the light which has traversed the glass is not quite pure, so that that image of 
the slit which should be illuminated only by light of wave-length, say, A = -433, is also, owing to 
reflections from dust particles, &c., illuminated by light of other wave-lengths which has experienced a 
less absorption. 

* BREDIG, ' Zeitschr. f. Electrochemie,' 4, pp. 514, 547. 

t EHRENHAFT, loc. cit., p. 506. 

J BARUS and SCHNEIDER on "The Nature of Colloidal Solutions," 'Zeitschr. f. Phys. Chem.,' VIII., 
p. 278. 

Tabelle 5, loc. cit., p. 296. 



VOL. CCV. A. 2 L 



258 



MR. J. C. MAXWELL GARNETT 



TABLE V. Index of Refraction of Colloidal Solution of Silver for Sodium Light 

(X = -589). 



Solution. 


Percentage of 
silver. 


Percentage 
of foreign salts. 


Temperature, 
C. 


n. 










18-0 


1-3306 










18-2 


1-3315 




1-16 


0-18 


18-6 


1-3369 


Silver Solution* . . . < 


1-16 


0-18 


18-6 


1-3363 




1-16 


0-18 


18-6 


1-3369 




1-16 


0-18 


17-0 


1-3363 


Water J 








18-7 


1-3331 










19-0 


1-3333 



* The solutions were prepared by CAREY LEA'S method of precipitating silver nitrate with ferrous 
citrate they were subsequently dialysed for 60 hours. 

Thus the mean refractive index of silver in water at 18'6 was n = T3367, while 
the refractive index of water at 187 was v = 1-3331. Taking the specific gravity of 
silver as 10, the volume proportion silver was /x = '00116. 

The values of the functions and a! for sodium light and water at v = T3331 are, 
according to Table II., a= 1-571 and a' = 1-333. Substituting these values of v, p., 
and a in equation (10), namely 



we obtain 



n' = *(l + f/ia), 
n' = ^(1-00273) = 1-33674. 
Similarly, from equation (9), 

n" v \ 1 H ua' 

2f 
we have 

n" = v (1-002078) = 1-33587. 
Comparison of these values of n' and n" with the observed value, namely n = 1'3367, 



ON COLOURS IN METAL GLASSES, ETC. 259 

requires that practically the whole of the silver must have been in suspension in the 
form of small spheres.* 

Once more, CAREY LEAt prepared suspensions of silver in water by precipitating 
the silver from the nitrate by means of a mixture of ferrous sulphate and sodic citrate. 
He describes how, after careful washing, the silver frequently " dissolved," forming a 
liquid which varied from red to yellow^ and was generally blood red ; he adds : 

" On one occasion the substance was obtained in a crystalline form. Some crude red solution had been 
set aside in a corked vial. Some weeks after the solution had become decoloured with crystalline deposit 
on the bottom, The bottle was carefully broken ; the deposit, examined by a lens, consisted of short 
black needles and thin prisms." 

If, then, the diffused particles of silver when aggregated and precipitated had 
become crystalline, they must before have been in the form of nascent crystals, and 
for gold and for all the substances examined by VOGELSANG, such nascent crystals 
were spherical. 

7. Blue Reflection from the Stained Face of Silver Glass. 

When clear glass is flashed with silver glass, or when a clear glass is so stained on 
one face with silver that the volume proportion /A of silver does not gradually diminish 
to zero as we proceed inwards from the stained face, but that the stained region ends 
abruptly, a blue reflection from the interface can be observed if the glass is held with 
the stained face away from the eye. No blue reflection can be seen from the 
air-glass interface when the stain is held towards the eye. STOKES observed this 
blue reflection, and stated that the interface presented the appearance of being coated 
with a fine blue powder. || 

We proceed to examine whether the presence of small spheres of silver, which has 
been shown to account for the colour of the light transmitted by silver glass, will also 
account for this blue reflection. Consider, then, plane polarised light travelling in a 
medium of refractive index v' and directly incident on the surface, z = 0, of an 
absorbing medium whose optical constants are n' and K', where N' = n' (I IK'). Then 
we may take as the electric and magnetic vectors for 

* BARUS and SCHNEIDER (foe. cit., p. 297) make the following comment on their experiment: 

"KuNDT has found for normal metallic silver a refractive index of about 0'27. It would, therefore, be 
expected that the presence of the silver would diminish the refractive index of the water. It is by no 
means denied that it might be possible to explain the normal refractive indices of the above table in 
accordance with MAXWELL'S Theory of Light." 

The investigation in the text attempts to give such an explanation. 

t CAREY LEA, ' Amer. Journal of Science,' 1889, and 'Phil. Mag.,' 1891. 

I Cf. above, p. 243, especially second footnote. 

Cf. above, 1. 

|| STOKES, 'Collected Works,' vol. III., p. 316. 

2 L 2 



260 MR. J. C. MAXWELL GAKNETT 

Incident light : 

X = exp {tp (t-i/z/c)}, Y = 0, Z = 0, 

a = 0, /3 = v' exp {ip (tv'z/c)}, y = 0. 

Reflected light : 

X = B exp {ip (t+v'z/c)}, Y = 0, Z = 0, 



a = 0, /3 = z/B exp {ip (t + v'z/c)}, y = 0. 

Light inside absorbing medium : 

X = C exp {ip (t-Wz/c)}, Y = 0, Z = 0, 

= 0, /3 = N'G exp {ip (t-Wz/c)}, y = 0. 

Making X and /3 continuous at Z = 0, we have 

C=1+B, N'C = /(1-B). 
Hence 

B = 



Taking the square of the modulus, we have, for the value II of the ratio of the 
intensity of the reflected light to that of the incident light, 



R = (B)* = ="! ........ (12). 

' '' 2IJ 



If, now, the absorbing medium consist of minute spheres of metal embedded in a 
transparent medium of refractive index v, we have equations (10), namely, 



n' K ' = Sfjiv/3, n'= y(l+f/ta) ....... (10). 

Substituting these values of nV and of n' in (12) we obtain 

...l - - (13), 



in which powers of /t higher than the second have been neglected. 

Suppose first that v' = 1, so that we consider the reflection at the front face of the 
stained glass. Omitting powers of p. except the lowest which occur, we then have 
from (13) 



It appears from equation (14) that light is reflected from the stained glass almost 
as if the stain did not exist, the effect of the stain being slightly to increase the 
reflection of those colours (in the blue) for which, according to Table II., a is greatest. 



ON COLOURS IN METAL GLASSES, ETC. 



261 



Now, however, suppose that v' = v, so that the light is reflected at the interface 
between colourless glass and the same glass containing small spheres of metal. 
Neglecting p. 3 , equation (13) then reduces to 



(15). 



Since this expression for R contains no large constant term, the light from the 
interface will in this case be highly coloured in the case of those metals for which 
a 3 +4/8 2 varies greatly for different values of X. 

If, however, the absorbing medium contain molecularly divided metal, equations (10) 
are replaced by 

2 + " 2 - A (11). 



n" = 



Replacing 3/*/3 and 3/j.a. in equations (14) and (15) by (2 + v 2 )/v 2 . /3' and (2 + v 2 )/v 2 . a' 
respectively, we obtain, as the intensities of the light reflect from the front face of 
the stain and from the interface respectively, 



<>> 



(17). 



As before, it appears that when the stain is held towards the eye the reflection 
R/ is almost as if the stain were not there ; while when the stained face is away from 
the eye, the reflection is highly coloured. 

Sir WILUAM ABNEY has kindly measured for me the intensities R of light 
reflected from the interface between the unstained and stained regions of one of 
STOKES' specimens of silver glass. The values of R are given in the following 
table : 

TABLE VI. Blue Reflection from Silver Glass. Measured Value of 

v at D Lines = T532. 



A. 


Ro. 


A.. 


RO. 


A. 


Ro. 


4200 


25 


5000 


067 


5800 


014 


4300 


285 


5100 


050 


5900 


016 


4400 


290 


5200 


042 


6000 


018 


4500 


267 


5300 


032 


6100 


020 


4600 


237 


5400 


025 


6200 


021 


4700 


195 


5500 


020 


6300 


022 


4800 


146 


5600 


018 








4900 


095 


5700 


016 


6800 


022 



262 



ME. J. C. MAXWELL GAENETT 

Fig. 5. 
(1) E 



Blue reflection from silver glass. 
Calculated values : O- 
spheres in glass, v = 1 56 : 

(2) E' -r- molecules in glass, v = 1 56 : 

Observed values : x . 

(3) BO ~f~ observed : 




350 -400 -450 -500 



550 -600 



650 



700 



Fig. 5. 



The continuous curve shown in fig. 5 has been fitted to the plots of these values 
of E. . In the same figure are also shown the calculated values of E and of E/, 
obtained from equations (15) and (17) by means of the values of a 2 +4/3 2 and of 
a' 2 + 4/3 /2 given for silver and glass of refractive index v = I' 56 in Table II. The 
scales on which E and E' are represented are so chosen that the ordinates corre- 
sponding to X = '589 shall be the same as that for the continuous curve. 



ON COLOURS IN METAL GLASSES, ETC. 263 

It appears that while the graphs of R' and R widely differ, the positions of the 
respective maxima falling near X = '360 and X = '436 respectively, the graph of R 
closely resembles that of R 0) * the maxima of R and of R' occurring at almost the 
same value of X. We conclude that the presence of small spheres of silver throughout 
the stained region of the glass will account for the blue reflection ; and we thus 
confirm the view, to which absorption phenomena led us, that silver glass consists of 
a suspension of small spheres of silver in a colourless glass. 

Before leaving the consideration of the blue reflection from silver glass, it may be 
noticed that the light is not reflected as from a plane interface between glass and 
silver glass. Thus when the source of light is an electric arc, the blue colour is 
clearly discernible by an observer whose eye is not in the straight line determined by 
the ordinary law of reflection. This effect is due to the irregularity of the interface, 
the silver not having penetrated the glass to a uniform depth. AH alternative 
explanation, however, suggests itself, the blue colour might be due to independent 
radiation from discrete spheres (or molecules) of silver so far apart as not to form an 
optically homogeneous medium. The intensity of the emitted light would then be 
proportional to (a 2 +4/3 2 )/X 4 (in the case of spheres, or (a'- + 4/3'-)/X l in the case of 
molecules). Further, the blue colour would be equally visible if the light illuminating 
the discrete spheres (or molecules) entered the silver glass from the air side or the 
clear glass side ; and this is not the case. 

It is of interest to notice that while each individual sphere in glass radiates out 
light of an intensity proportional to (a*+ 4j6 2 )/X 4 , a surface separating a glass, containing 
many of the spheres to a wave-length of light, from a region of the same glass in 
which no spheres are present, reflects light with an intensity proportional to or + 4/3". 
This is due to the fact that the number of spheres (on the reflecting surface), the 
phase of the forced vibrations of which lies at any instant between given limits, is 
proportional to X 2 ; so that the intensity of the reflected light is proportional to X' 
times the intensity of the light emitted by a single sphere. 



8. Diffusions of Copper. The Nature and Form of the Suspended Particle*. 

We proceed to discuss the colours produced by diffused particles of copper in order 
to discover the cause of colour of copper ruby glass. The values of the expression 
nV//iX for v = 1-56, v = 1'5, and v = I'O given in Table III., are plotted in fig. 6, the 
maxima being determined as in the case of fig. 1 (cf. 5 above). As in the case of 
silver, these curves should fairly accurately represent the absorptions produced by 
copper spheres in glass v = T56, in glass v = 1'5, and by copper spheres or molecules 

* The fact that E increases from yellow to red, while E diminishes in the same range, would be 
accounted for if the black paper with which Sir WILLIAM ABNEY backed the stained face of the glass 
reflected 2 per cent, of the light incident on it. Further experiments are to be made on this. 



Fig. 6. COPPER calculated values of -^-. 



Observed values : x . 



264 MR. J. C. MAXWELL GARNETT 

Fig. 7. COPPER. 
( 1 ) K, observed for copper ruby glass Cu (X) : 

(1) Spheres (or molecules) in vacuo, v = 1 : 

(2) Spheres in glass, v = 1 5 : 

(3) Spheres in glass, v = 1 56 : 

Calculated values shown thus : Q. t v ~ 

(3) n -!L ! calculated for copper molecules in 

glass : 

Calculated values : O. 



(2) ~, calculated for copper spheres in glass, 



if 



- . 
tf 









.( 



60 

E 



ON COLOUKS IN METAL GLASSES, ETC. 265 

(copper vapour) in vacuo respectively. The absorption band in the yellow green 
shown by the top two curves in fig. 6 was observed by STOKES in the spectrum of a 
copper ruby glass. 

In fig. 7 the graphs of nV/X for glass (v = 1'5) and of H"K"/\* are reproduced from 
fig. 6 on such a scale as to have the same ordinate at the D line as that possessed by 
the continuous curve which has been fitted to the plots of the measured absorption K 
of the glass Cu (X). The curves in fig. 7 all have a minimum in the red or infra red 
and a maximum in the yellow-green ; but while that (nV/X) which represents the 
absorptions of spheres in glass has a secondary maximum near X '480, the dotted 
curve shows that the absorption of copper molecules in glass continues to increase till 
X< - 350. Also the maximum in the yellow green for the "sphere" curve occurs for 
approximately the same value of X as corresponds to the maximum observed absorption ; 
while the value of X at the maximum of the dotted ("molecule") curve is about lO^i/A 
less, and the latter maximum is much less marked than are the former two. Finally, 
the last readings obtained for K in the violet indicate that the continuous (observed) 
curve rapidly approaches a maximum near X = '480. 

We conclude that copper ruby glass is coloured by metallic copper,! and that the 
greater part of the copper is present in the form of small spheres, although some 
probably remains in the form of discrete molecules.| 

The manufacture of copper ruby glass closely resembles that of gold ruby. Like 
gold ruby, the copper ruby glass becomes turbid if kept too long at a high temperature. 
This turbidity is also probably due to the formation of crystallites by the coagulation 
of small spheres, since, when the conditions necessary for the development of turbidity 
are long maintained, actual crystals, apparently of copper, are formed in the glass. || 

9. Colouring Effects of the Radiation from Radium, Cathode Rays, &c. 

It has long been well known that cathode rays produce a blue-violet coloration in 
soda glass. Soda glass tubes, after containing the emanation from radium, show the 

* The graph of V/A for v = l can, by increasing all the ordinates in the proper constant proportion, be 
changed into the graph of w'V'/A for any value of A. Of. 3 above. 

t STOKES (' Math, and Phys. Papers,' vol. IV., p. 242) supposed that the colouring agent was suboxide 
of copper. The blue colour exhibited by overheated specimens of the glass (lo>;. cit., p. 243) is probably 
caused by the coagulation of the small spheres into crystallites and crystals which reflect out the red light. 

| Measurements will have to be made with ultra-violet light in order to determine how much copper 
remains in the molecularly subdivided condition. 

Of. above, 5, p. 251. 

|| Of. 'Phil. Trans.,' A (1904), p. 392. Some of the crystalline glazes made by Mr. BURTON at 
PILKINGTON'S tile works exhibit the same effect. I have seen a pot with a copper glaze in parts of which 
the copper was apparently reduced, for in passing from the colourless glaze (where the copper was not 
reduced) into regions where the reduction had been effected, a deep red (copper ruby) was first reached ; 
that colour increased in intensity until, in the central portions of the region, crystals, apparently of copper, 
could be seen. 

VOL. CCV. A. 2 M 



266 ME. J. C. MAXWELL GARNETT 

same colour, and crystals of each salt acquire iinder cathode rays a beautiful violet 
tint.* Experiment has also shown that exposure to the emanation from radium gives 
to gold glass a ruby colour, to silver glass a yellow colour, and to potash glass a brown 
colour. 

Now we have seent that a molecularly subdivided metal possesses the same colour 
by transmitted light whatever be the nature of the surrounding transparent medium, 
supposed non-dispersive and isotropic. This colour may be called the vapour- colour 
of the metal. It has further appeared that although the transmitted colour of a metal 
subdivided into small spheres, many to a wave-length of light, does depend on the 
refractive index v of the medium in which the small spheres are " embedded," yet 
this colour approaches to the vapour-colour as v approximates to unity. As is shown 
by the dotted curve in fig. 1, the vapour-colour of gold must be red.| The colour of 
glass containing molecularly distributed gold is thus red,;}; although when the gold is 
collected into spheres the glass is pink. Similarly, reference to the relative values of 
/3'/X in Table II. shows that the vapour-colour of silver is yellow. Glass coloured 
by small spheres of silver is also yellow. Again, Professor R. W. WOOD showed to 
the British Association^ in Cambridge that the vapour-colour of sodium is violet, this 
colour being due to the absorption at the D lines. This violet colour is also produced 
at the cathode in the electrolysis of sodium chloride, || the molecules of sodium formed 
at the cathode being distributed throughout the water in its neighbourhood and 
giving rise to the vapour-colour. 'I Analogy with the cases of gold and of silver 
indicates that small spheres of sodium would produce in glass a colour not greatly 
different from the vapour-colour produced by the molecularly subdivided metal. 

Thus the colours developed in gold, silver, or soda glass by the radiation from the 
emanation from radium are approximately the same as the colours which would be 
given to the glass by the presence of the reduced metal, either molecularly divided or 
in small spheres (nascent crystals). 

It is therefore very probable that the metal in the glass is reduced by the action of 
the radiation. This view finds considerable support in the discovery of VILLARU,** 
that cathode rays exert a reducing action, as well as from the fact, already cited, tf 
that ELSTER and GEITKL found the salts of the alkali metals, which had been coloured 
by exposure to cathode rays, to exhibit photo-electric effects as if they contained 
traces of the free metal. 

* GOLDSTEIN, ' WIED. Ann.,' liv., p. 371, 1898. 

t Fide ante, p. 243. 

I Or yellow ; see the second footnote, p. 243. 

August, 1904. 

|| Cf. J. J. THOMSON, 'Conduction of Electricity through Gases,' pp. 495, 496. 

IT BUNSEN found that common salt, after heating to about 900 C., exhibited a violet colour, due 
apparently to the reduced metal, although BUNSEN suggested a, subchloride, 
** 'Journal de Phys.,' 3' Series, VIII., p. 140, 1899. 
tt See 'Phil. Trans.,' A, 1904, p. 400. 



ON COLOURS IN METAL GLASSES, ETC. 267 

Sir WILLIAM RAMSAY, when I first called his attention to the explanation of the 
coloration of glass by radium which is afforded by supposing the radiation to reduce 
metal in the glass, suggested that the reduction might be effected by the discharge 
of free ions of the metal. Since that time the further evidence that has accumulated 
seems to 'favour the truth of this theory. Thus, as all the colour-changes from pink 
to blue exhibited by gold glass can be imitated with suspensions of gold in water, 
the glass appears to behave as a liquid, although a very viscous one ; and it seems, 
therefore, reasonable to suppose that the salt of a metal which will dissociate in 
water will dissociate also in glass. As an alternative hypothesis, we might suppose 
the compound molecules broken up by the rays. But, were this the case, the a-rays 
would be far more efficient than the /3 in producing the colour. And this is not 
true ; for the coloration produced in the splinters of gold and silver glass, as well as 
in soda and potash glasses, are not, apparently, stronger on the sides of the glass, 
but seem to be of uniform strength throughout. From this it appears that the /8-rays 
are alone capable of producing the colour. This is in accord with the former 
hypothesis. For the ions of the metal in the glass would be positively charged, and 
their discharge by the negatively-charged /3 particles (or cathode rays) would change 
them into molecules just as the sodium ions in the electrolysis of common salt are 
discharged at the cathode, and thus are transformed into molecules of sodium, 
imparting a violet colour to the water and capable of forming caustic soda. 

It appears, therefore, possible that all glasses contain free ions of metal, and that 
it is by the discharge of these ions, and consequent reduction of the metal, that 
cathode and Becquerel rays are able to produce coloration in them. 

10. Numerical Values of the Optical Constants of Media containing Large Volume 

Proportions of Certain Metals. 

The preceding sections of this paper have treated only of the optical properties of 
those media for which the volume proportion, //., of metal is very small. The 
consideration of media in which p. may have any value up to unity will now, however, 
be resumed, in order to discover what may be the physical explanation of those 
colours and changes of colour which FARADAY,* BEILBY,! and others have found to 
be exhibited by thin metallic films. In 11 of the former communication J the 
question whether films built up of small spheres of silver or of gold would, for any 
given volume proportion of metal, transmit red or yellow light more easily, was dis- 
cussed, and the conclusions reached were compared with the results of Mr. BEILBY'S 
experimentsf on the effect of heat on thin films of metal. The present section 
extends the scope of that enquiry. 

* Bakerian Lecture for 1857, 'Phil. Trans.,' A, 1857. Reprinted in FARADAY'S 'Researches in 
Chemistry and Physics,' pp. 391 et seq. (Reference will be made to the pages of the reprint.) 
t 'Roy. Soc. Proc.,' vol. 72, 1903, p. 226.. 
t 'Phil. Trans.,' A, 1904, p. 415. 

2 M 2 



26 g ME. J. C. MAXWELL GARNETT 

It has been shown that the optical properties of a metal, so diffused in vacuo (v = 1) 
that p. has some definite value, are the same whether the microstructure be amorphous 
(molecularly sub-divided) or consist of small spheres, these optical properties being 
in either case deducible from equation (7), p. 241.* If then, in accordance with the 
notation adopted in the former communication (pp. 403 et seq.), the accents' hitherto 
used to denote the optical constants, n and HK, when p. differs from unity, be now 
omitted, and the values of those constants corresponding to any particular value /*' 
of p be denoted by a suffix (e.g., HK^^), the values of n and HK are given by 
equation (17), p. 404, t namely, 



a ; 



where, as in equation (13'), p. 403, t 



- { n'(K'-l)-2}' + 4nV > K(^-l)-2 

By these equations the values of n and UK, determining optical properties of 
amorphous or " small-sphere " metallic media of any density, may be calculated for 
light of wave-length X, in terms of the values of n^ =l and of nK IL=l for the same mono- 
chromatic light. The values of n and of UK for gold and for silver have already been 
calculated for all values of \L in the case of red light (X = '630) and in that of 
yellow light (X = '58 9). The results are given in Table IV. of the former com- 
munication. | But in order to obtain a true conception of the colours of such media, 
corresponding calculations must be effected for other colours also. 

Now, in the case of silver, the numerical values of all those functions of HK^I and 
M=1 which have hitherto been calculated for the case of v = 1 those functions, in 
fact, which relate to molecules or small spheres of silver in vacuo vary continuously 
from red (X = -630) to blue (X = '450). If, therefore, the values of n and UK 
corresponding to X = '450 and X = '500 be now calculated for all values of p., the 
values of n and n/c for other colours may be obtained approximately by interpolation 
between X = '630 and X = '450. 

The values of n and UK corresponding to X = '450 and X = '500 have therefore 
been calculated for certain values of /A, by means of equations (18) and (19). The 
values of ?i/c /1=1 and n^ =l used for the calculations were carefully determined by 
B. S. MINOB. The results are tabulated below (Table VIII.). 

In the case of gold it is not so easy to apply this method of interpolation. 
The values of n and HK corresponding both to blue (X = '458) and to green (X = '527) 

* 'Phil. Trans.,' A, 1904, equation (16), p. 403. 

t ' Phil. Trans.,' A, 1904. 

I ' Phil. Trans.,' A, 1904, p. 406. 

Loc. cit. (vide ante, Table II). 



ON COLOUES IN METAL GLASSES, ETC. 



269 



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270 MR. J. C. MAXWELL GARNETT 

have been calculated ; but the values of nK^ =l and n^i used for the purpose are 
those given by HAGEN and RUBENS,* and are not by any means so accurate as 
those which MINOR has determined for silver.! The results are included in Table VII. 

We return to the consideration of the transmission and reflection of light by a 
metallic film. We confine our present attention to films the microstructure of which 
is either amorphous or consists of small spheres of metal ; the films in question are 
thus optically isotropic. Suppose that, as explained in the preceding section, the 
optical constants of the film are n and K when its specific gravity is p. times that of 
the metal of which it is composed. 

When light of wave-length \ in vacua is directly incident on such a film, ot 
thickness d, let R ft and T denote the ratios of the intensities of the reflected and of 
the transmitted light to that of the incident beam. Adopting the analysis already 
given in the previous paper, p. 409, we suppose the film to be bounded by z = and 
z = d, and that 

Incident wave is 

E = 0, exp {ij> (tz/<-)}, ; H = -exp {ip (t-zjc}, 0, 0. 
Reflected wave is 

E = 0, B exp { ip (I + z/c)} , ; H = B exp { ip (t + z/c) } , 0, 0. 
Wave in film, i.e., hot ween z = and z = d, is 

E = 0, A' exp {q> (/-c/V)} t-B' exp { lp (t + z/V)}, 0, 

H = -c/V[A' exp {tjp(-*/V)}-F exp {q>(f + z/V)}], 0, 0. 

Transmitted wave is 

E = 0, Cexp{ip(*-z/c)},0; H= -(! exp [q, ((-z/c)}, 0, 0, 
where c/V = H (1 IK). 

We shall suppose:]: that Trdn K /\> 1, so that we shall be correct within 2 per cent. 
when we neglect B' in comparison with A'. The boundary conditions at 2 = 0, 
namely the continuity of the components of E and H which are parallel to the 
interface, then give 

1 + B = A'; (l-B) = e/V. A' = (!-) A'. 
Eliminating A' we obtain, by taking the squares of moduli, 



* Loc. cit. 

t Cj. above, 4. 

| Of. 'Phil. Trans.,' A, 1904, p. 409. 



ON COLOURS IN METAL GLASSES, ETC. 271 

In equation (26), on p. 409,* we have already proved that 

T = I 1 2 - 16^(1 + *") -^./A (9 - \ 

s 



If we write 

M 16n 2 (l + K 2 ) , 

-{(l + n) 2 +nV} 2 
equation (21) may be written 

T = Mo e -""'"" /A ......... (23). 

Equations (20) and (21) are thus correct within 2 per cent, for directly incident visible 
light, and for /A = 1 in the case of gold if c/>91ju//, or in the case of silver if 
(/> 60/J./A, where Ip-p EE 10~" millim. 

For convenience of reference the corresponding results for obliquely incident light 
are given below. Let be the angle of incidence. When the incident light is 
polarised in the plane of incidence, the ratios R, T of the intensities of the reflected 
and of the transmitted beams to that of the incident light are given by 



' 8ay ..... (2o) ' 



where u and v are defined by the equation 



(u, v) cos (9 = [{(nV-1 + sin 2 0} 2 + 4nV} + (n 3 /?^! + sin 2 ^)] 5 . . (20). 
v 2 

When, however the incident light is polarised perpendicular to tlie plane of 
incidence, the corresponding ratios are given by 



where 

u'-<.v'={n(l-i K )YI(u-<.v) ........ (29). 

Putting 9 = 0, we obtain 

R = If = H, h T = T' = T , 

u = u' = n, v = v' = HK. 

It appears from equation (23) that the colour of the light transmitted by a metallic 
film, although principally dependent on the values of nK/k for different values of X, is 
also affected by the corresponding values of M . The thicker the film, however, the 
less important is M in determining the colour. 

* 'Phil. Trans.,' A, 1904. 



272 



ME. J. C. MAXWELL GARNETT 



The values of n/c/\, calculated from Table IV. of the former paper,* using however 
new and more accurate values in the case of silver with red light, and from 
Table VII. above, are shown in Table VIII. The corresponding values of M 
are given in Table IX., in which table the values of the reflecting power R have 
also been included. 

In order to facilitate the consideration of the colours which should, according to 
the above analysis and calculations, be exhibited by gold and silver films when their 
specific gravities vary but their microstructures remain amorphous or granular (small 
spheres), graphs of n/c/\, of M , and of R are given in the accompanying figures 
(figs. 8, 9, 10, 11, 12, and 13). In these figures the abscissse represent the volume 
proportion, /A, of metal, and the ordinates the value of the function. The curves 
have been fitted to the plots of the numerical values shown in Tables VIII. and IX. 
In each case the positions of the plots of calculated values have been indicated by 
small circles. 

TABLE VIII. Value of n K /K. 



~a 

43 

y> 

M 

<5 


o 
"3 
U 


-4 


i i 

II 
a. 


ci 

11 

a. 


* 

II 

3, 


id 

II 

a. 


o 

II 
a. 


i-^ 

II 
a. 


oo" 

II 
a. 


a> 

II 
a. 




II 
a. 


,-H 1 

II 

a. 


1 
a 




Blue . 


458 


420 


879 


1-845 


2-279 


2-637 


2-908 


3-099 


3-240 


3-319 








r ' 

"3 i 


Green . 


527 


-.360 


861 


2-432 


3-149 


3-526 


3-646 


3-642 


3-592 


3-529 


3-524 


599 


O 


Yellow 


589 


046 








896 


2-555 


6-90 


6-45 


5-42 


4-79 


6-47 


685 




Red . 


630 


022 








381 


960 


4-56 


7-95 


5-96 


5-00 


7-76 


734 




Blue . 


450 


064 





902 


3-50 


10-16 


7-81 


6-49 


5-76 


5-30 


9-17 


561 


|H 

to 

\ 


Green . 


500 


022 


053 


197 


431 


1-401 


12-557 


8-901 


6-850 


5-882 


11-585 


693 


a 


Yellow 


589 


008 








112 


238 


762 


14-84 


8-33 


6-23 


13-52 


791 


1 


Red . 


630 


006 





046 


082 


163 


444 


4-885 


9-005 


6-286 


13-599 


822 



'Phil. Trans..' A, 1904, p. 406. 



ON COLOUKS IN METAL GLASSES, ETC. 



273 



TABLE IX. 



M 

" 



/c ~ _ 

a > ' u ~ 





Colour. 


1 
a 




/=! 


^=4 


P--6 


/x=-6 


/x=-7 


.>=-8 


^=9 


./i=l-0 


/*--. 
a 




Bed 1 


822^ 


' Mo 


985 


801 


695 


560 


380 


123 


430 


858 


087 




A -630 j 


I 


. RO 


007 


105 


167 


252 


385 


669 


928 


953 


792 




Yellow 1 


79lJ 


; MO 


984 





675 


529 


331 


105 


563 


972 


100 


Silver "{ 


A-589 j 


I 


RO 


008 





179 


274 


419 


800 


930 


951 


778 




Green "1 


G93<J 


Mo 


979 


725 


573 


365 


184 


634 


1-056 


1-384 


174 




X-500 J 




Ro 


010 


149 


245 


403 


736 


881 


916 


932 


709 




Blue 1 


561< 


M 


969 


592 


367 


423 


894 


1-29 


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1-79 


308 




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238 


432 


716 


824 


867 


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620 


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247 


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215 


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406 


374 


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239 


335 


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134 


188 


242 


294 


343 


387 


427 






VOL. CCV. A. 



2 N 



274 



ME. J. C. MAXWELL GARNETT 



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ON COLOURS IN METAL GLASSES, ETC. 



275 



Fig. 10. GOLD M . 



Fig. 11. SILVER M . 



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'276 



MR. J. C. MAXWELL GAKNETT 



Fig. 12. GOLD RQ. 
Red (A =-630): 
Yellow (A =-589): - 

Green (A =-527): 

Blue (A= -458): 



Fig. 13. SILVER RO. 
Red (X= -630): 
Yellow (A =-589): 

Green (A =-500): 

Blue (A. = "450): 




I 



ON COLOUES IN METAL GLASSES, ETC. 277 

11. Colour Changes Caused by Heating Metal Films. 

In the Bakerian Lecture* for 1857, FARADAY described a, number of experiments 
concerning the colours which gold and other metals were, in various conditions, 
capable of exhibiting. 

Mr. G. T. BEILBY'S investigations on the colour and structure of films of metal are 
described in his paper on " The Surface Structure of Solids."t 

The average thickness of the gold leaf which FARADAY used in his earlier 
expei'iments was about 90 /i/i.| Reference to p. 271 above will show that, with a 
probable error of 2 per cent., the optical properties of such a leaf will be subject to 
the analysis given in 10 above. 

Thus, for example, if we assume that, in a gold leaf as it leaves the beater, the 
gold is in an amorphous state, its colour by directly transmitted light is that for 
which T , as given by equation (23), namely 

T = M u exp {-4ml. riK/X} (23), 

is a maximum. If, further, the metal has its normal specific gravity, so that /j. = 1, 
the values of nx/K and of M in this equation are those given for p, = 1 in Tables VIII. 
and IX., or figs. 8 and 10. 

Now, when /JL = 1, the value of n/c/A. is much smaller for blue and green than for 
yellow and red, and is slightly smaller for blue than for green ; while the value of M 
is greater for green and blue than for yellow and red, and is considerably greater for 
green than for blue. Thus both the factors of T in equation (23) are greater for 
blue and green than for yellow and red. The former colours therefore predominate 
in the transmitted light. Further, in very thick films, for which n/c/A. is of supreme 
importance, blue should, in the transmitted beam, predominate over green ; while in 
thinner films, on account of the greater value of M u for green than for blue, green 
light should be more intense. 

FARADAY found that all his gold leaf appeared olive-green by transmitted light. 

Again, Table IX., or fig. 12, shows that the reflecting power, R , is, when p = 1, 
much greater for red and yellow than for green and blue ; and this result is again in 
accordance with the observed colour of gold leaf by reflected light. 

FARADAY, however, states that gold leaf still appeared green by transmitted 
light when its thickness was reduced to only 10 JU./A or 5 pp,. Now equation (24) of 
the former communication, || namely, 

T = l-47rd.n 2 K /\, 

* Reprinted from the 'Phil. Trans.' in his 'Researches in Chemistry and Physics,' p. 391. References 
will be made to the pages of this reprint." 
t Glasgow, 1903. 
t Loc. tit., p. 394. 
Loc. tit., p. 395. 
|| 'Phil. Trans.,' A, 1904, p. 408. 



278 MR. J. C. MAXWELL GAKNETT 

shows that, for a film of such thinness, the intensity T of the transmitted light is 
greatest for red light.* This red colour has been seen both by FARADAY! and by 
BEILBY| in parts of their green films. FARADAY says the red colour was extremely 
faint but appeared to have an objective reality, while BEILBY describes the effect as 
that of " an irregular film of pink jelly." 

It appears that extremely thin films of gold are, by surface tension, drawn up into 
green patches, leaving larger areas covered by an almost transparent, but faintly red, 
film. The effect on the unaided eye is that of a transparent green. 

The silver leaf used by BEILBY was over 300 p,^ thick. It therefore comes well 
inside the range for which the analysis of 10 applies. Now Table VIII. , or fig. 9, 
shows that, for amorphous silver of normal specific gravity (//. = 1), /c/X is least for 
the more refrangible rays. Again, Table IX., or fig. 11, shows that, for p. = 1, M is 
greatest for the same rays. It follows therefore, from equation (23) above, that, on 
both these accounts, the light transmitted by silver leaf should be blue ; and, in fact, 
silver leaf transmits a deep blue light. The approximately equal values of the 
reflecting power, R , shown in Table IX., or fig. 13, for /A = 1, correspond to the 
almost colourless reflection from polished normal silver. 

Consider now the colour changes which, according to figs. 8 to 13, deduced from 
the calculations of 10, should accompany a diminution in the density of gold and 
silver films from its normal value (/u. = 1) to zero (p. = 0). This diminution of density 
may be conceived either as an increase of the distance between adjacent molecules or 
as due to the aggregation of groups of neighbouring molecules into small spheres. 
For geometrical considerations show that so soon as two spheres form adjacent to one 
another in an otherwise amorphous mass of metal, the density of the mass must begin 
to diminish. And it has been shown that the calculations in question are applicable 
whether the metal is in small spheres or in an amorphous state, and thus when it is 
partly in the one condition and partly in the other. 

Taking first the case of gold, it appears from figs. 8 and 10, in conjunction with 
equation (23), that, as /x begins to diminish from unity, the absorptions of red and 
yellow light increase rapidly, owing both to the increase of HK/\ and to the decrease 
in M . Meanwhile, owing to the decrease of the ratio of M (green) to M (blue) and 
to the increase of (wic/X) (green) (w/c/X) (blue), the relative intensity of green to blue 
in the transmitted beam diminishes. Thus the first effect is to make the transmitted 
light bluer, and this effect continues until //. = about 75. As p continues to diminish 
below this value, the absorption of red rapidly decreases until, at /u, = '68, in a very 
thick film, the absorption of red has become as small as that of blue. The film is 

* Cf. Table IV., p. 406 of former paper, and Table VIII. above, 
t Loc. cit., p. 400. 
I Loc. cit., p. 40. 

When exp ( - iird . WK/A) is the dominating factor in T . The corresponding value of /* is less in 
thinner films for which M is very important. 



ON COLOURS IN METAL GLASSES, ETC. 279 

then purple. As p. still further diminishes, the relative absorption of red continues to 
become small, so that the film becomes pink. Finally, at p. = 0, the absorption of 
green is less than that of blue, and the colour has changed from pink to red.* It is 
further seen, from fig. 12, that the reflecting power E, has, as p, began to diminish, 
become more yellow. At p, = '60, when the colour of T is still purple or pink, the 
colour of R has become green ; and thenceforward R remains green as p. diminishes 
from '6 to zero. 

Similar consideration of figs. 9 and 11 shows that in the case of silver, as p. 
begins to diminish from unity, the colour by transmitted light becomes at first bluer, 
then changes to purple in the neighbourhood of p, = '8, and thence, through pink, to 
red or " amber " as p, further diminishes to /A = 0. In fact, it appears from the four 
colours for which calculations have been made, that there is, for any value of p., a 
well-defined absorption band at some position in the (visible or invisible) spectrum, 
and that, as p. diminishes, the position of this absorption band moves from the 
infra-red through the visible spectrum towards the shorter wave-lengths, being 
at X = -630 for p, = about '83, at X = "589 for p, = about '80, at X = '500 for 
p, = about '69, and at X = '450 for p. = about "55. Fig. 13 shows that the colour of 
the reflected light becomes distinctly blue at about p = '75, and remains blue down 
to p. = 0. 

With a view to determining what may be the explanation of the colours and 
changes of colour exhibited by gold and silver films, we have now to compare the 
latter colours with those which we have found above to be consequent upon a mere 
isotropic change in density. 

BEiLBYf has prepared gold films by using paints in which " the metal had been 
brought into solution in an essential oil." Having smoothly coated a plate of glass 
or mica with the paint, he heated it to a temperature of about 400, thereby driving 
off the oil and other volatile constituents. A film of pure gold with full metallic 
reflection, and transmitting green light, is left adhering to the glass. 

When these films are kept at a high temperature for some time, they change colour. 
By transmitted light, the original olive-green colour becomes at first bluer, then 
changes to purple, in which, as the annealing process is still continued, the red 
predominates more and more over the blue, until finally the purple has given place 
to pink. The reflecting power of the film has, meanwhile, diminished. But the 
colour of the light reflected from the blue films remains yellow, while the pink films 
reflect a green colour. I have before me a gold film prepared in this way and 
subjected to lengthy annealing. By transmitted light it appears striated with pink 
and blue bands. By reflected light the blue striae become golden, but the pink 
striae green. Under the microscope the film appears continuous, and is quite thick. 

These colour changes, both with transmitted and with reflected light, are just 

* Or yellow, if the colour is faint. See the second footnote on p. 243 above. 
- t Loc, cit., p. 40. 



2go MR. J. C. MAXWELL GARNETT 

those which have been shown above to be consequent upon a continuous diminution 
in the density of a gold film, which throughout remains either amorphous or 
"granular" (i.e., possessing a microstructure of small spheres). The view that the 
film is initially amorphous or granular, and that heating diminishes its density, is 
supported, as has already been pointed out,* by the fact that the curves in figs. 8 
and 10 show that the absorption of light increases rapidly as /* begins to diminish 
from unity, while BEILBY'S films exhibited just such an increase of absorptive power 
when first heated. This view is also in accordance with the loosening of structure 
which is suggested by the great decrease in electric conductivity which accompanies 
heating. But direct evidence of the correctness of the view that heating produces 
decrease in density is not wanting, for BEILBY! has estimated the thickness of a film 
which had been annealed to the purple stage. He found, by weighing the gold from 
a given area, that, had the density of the gold been then normal (p = 1), the film 
would have been lGO/x/.t thick, whereas, under the microscope, the thickness seemed 
to be much greater than this. The density of the gold in the purple film thus 
appeared to be less than in the normal green films. 

We conclude, therefore, that (a) the films, as first prepared, are amorphous or 
granular in structure; and (/*) heating diminishes the density of the film, while 
pressure is able to increase the density ar/ain.^ 

Further, BEILBY found t that, when the heating of a film was continued after it had 
reached the purple stage, " the film assumes a frosted appearance by reflected light 
and becomes paler by transmitted light." The frosted surface appeared, under the 
microscope, to consist of granules at least lOO/x^a in diameter. This phenomenon 
suggests that in the earlier stages of annealing, smaller granules were formed, which, 
as annealing proceeded, ran together to form larger granules : and the formation of 
such minute granules, while, according to our analysis, it does not aft'ect the optical 
continuity of the film, will explain the diminution in density which occurs on heating. 
It is, therefore, most probable that (c) tl\e diminution in density produced by heating 
is effected by the passage of metal from the amorphous to the granular phase and the 
growth of the larger granules at the expense of the smaller; and the increase in 
density produced by pressure may be accompanied by the passage of metal from the 
granular to the amorphous phase. \ 

The optical properties of the films of gold whicli FARADAY produced by reducing 
that metal from its solution by means of phosphorus, tend to show that these films are 
composed of amorphous or granular gold of density less than the normal. The films 
appeared to consist of pure gold ;|| when first prepared the films appeared of a grey 

* 'Phil, Trans.,' A, 1904, p. 415. 

t IMC. cit., p. 41. 

I Of. the effect of pressure on FARADAY'S " phosphorous " films after heating see next page. 

[Note added 31st August, 1905. Subsequent analysis has, however, shown that a sufficient flattening 
of the granules would cause the colours of the standard metal (//. = 1) to be exhibited.] 

|| FARADAY, loc. cit., p. 408. 



ON COLOURS IN METAL GLASSES, ETC. 281 

colour, which was frequently resolvable into a mixture of green and amethystine 
striae. These colours would be shown by an amorphous or granular film for which 
the density was in parts as low as p. = 7. Moreover, such a structure agrees with the 
fact that " the films did not sensibly conduct electricity " and that " the films cannot 
be regarded as continuous."* FARADAY further statest that, though they are certainly 
porous to gas and to water-vapour, the films have evident optical continuity. 

Heating diminished the conducting power and changed the colour to amethyst or 
ruby, just as with BEILBY'S films, pressure, which we should expect to increase the 
density of the film, changed the transmitted colour to green and increased the 
reflecting power ; and these are precisely the changes which would, according to 
calculation, accompany an increase in /A to the neighbourhood of unity in the case of 
an amorphous or granular film. 

Closely allied to these phosphorous films are the deposits of gold on glass which 
FARAD A Yj obtained " by deflagrating a gold wire by explosions of a Leyden battery." 
" There is no reason to doubt that these deposits consisted of metallic gold in a state 
of extreme division." This method of preparing these deposits is similar to BREDIG'S 
method of obtaining suspensions of gold in water ; it is, therefore, to be expected that 
the deposits consist of small spheres of gold .together with some large crystallites. 
The films were so discontinuous as to be unable to conduct electricity ;|| but they were 
such as to present an optical continuity.il FARADAY sums up their colour changes as 
follows : 

" Fine gold particles, loosely deposited, can in one state transmit light of a Hue-grey colour [/j. = about 8], 
or can by heat be made to transmit light of a ruby colour [/* < 7], or can by pressure from either of the 
former states be made to transmit light of a green colour,** all these changes being due to modifications 
Of gold as gold and independent of the presence of the bodies on which for the time the gold is supported." 

It appears, therefore, that the conclusions (a), (b), (c), arrived at on p. 280 for 
BEILBY'S films, are also applicable to FARADAY'S "phosphorous" films and to 
FARADAY'S " deflagration " films. 

One more experiment of FARAD AY'stt on coloured gold deposits remains to be 
noticed. When a drop of solution of chloride of gold is evaporated in a watch-glass 
until the gold is reduced, a portion of the gold is generally found to have been carried 
by the vapour on to the neighbouring part of the glass. This part has the ruby tint ; 
and we have seen that a ruby tint is characteristic of the light transmitted by 

* Loc. cit., p. 407. 

t Loc. cit., p. 439. 

J Loc. cit., p. 401. 

Cf. above, p. 252, and footnote, p. 255. 

|| Loc. cit., p. 402. 

U Loc. cit., p. 439. 

** Probably /A = 1 nearly ; but see fourth footnote on p. 280, above, 
ft Loc. cit., p. 428. 
TOL. COV. A. 2 O 



282 MR. -I. C.' MAXWELL GARNETT 

amorphous or granular gold, the density of which is in the neighbourhood of '6 of 
that of normal gold. 

The similarity of this method of preparing a metallic film with \L < 1 to that by 
which Professor R. W. WOOD prepared the sodium and potassium films, described in 
12 of the former communication,* is deserving of notice, and, from a different 
standpoint, tends to confirm the view there expressed as to the physical nature and 
structure of Professor WOOD'S films. 

The conclusions (a), (b), (c) arrived at above (p. 280) as to the effect of heat 
and pressure on metallic films do not apply only to gold, as the following observations 
on silver films show. FARADAY! obtained silver films by reducing silver from a 
solution of the nitrate. The thinner parts of these films transmitted light of a 
" warm brown or sepia tint [//, < '8]. Pressure brought out the full metallic lustre 
and converts the colour from brown (ju, < '8] to blue [p. > '8]." The behaviour ot 
these films corresponds to that of the gold films obtained with phosphorus. Again, 
ft. W. WOOD| prepared films by chemically depositing silver on glass. These films, 
as originally prepared, show the same reddish-brown colour by transmitted light, and 
have a good blue-green reflection. It has been shown above that both these colours 
are characteristic of amorphous or granular silver, for which p. is appreciably less 
than - 8. These films showed no electrical conductivity ; so that, as in the case of 
BEILBY'S gold films, || the evidence of a loose structure afforded by the colours 
exhibited is confirmed by the evidence from conductivity. 

12. The Exceptional Case of Beaten Metal Leaf. 

There is one class of metallic film which, when heated, does not exhibit the colour 
changes that, according to our calculations, correspond to a gradual diminution in 
the density of the film. To such films the conclusions (a), (b), (c) of p. 280 do not 
directly apply. Instead of being obtained from finely divided metal by chemical 
deposition, deflagration, &c., the films in question are prepared by beating sheets of 
the solid metal into thin leaves. 

FARADAY IF observed that heat caused gold leaf to lose its olive-green colour and 
silver leaf to lose its deep blue colour, the films at the same time becoming more 

* Loc. cit., p. 412. 

t Loc. cit., p. 409. 

| 'Phil. Mag.,' August, 1903. The silver was prepared by the method of CAREY LEA (' Amer. Journ. 
of Sc.,' 1889). A further memoir on WOOD'S silver films is now in course of preparation. 

Of. BARUS and SCHNEIDER, ' Zeitschr. f. Phys. Chem.,' VIII., p. 285, 1891, who attempted to 
measure the conductivity of a silver film prepared by CAREY LEA'S method, and found that, so soon as a 
drop of the silver suspension dried, so that the charged particles of silver could no longer move about, the 
conductivity of the drop vanished. 

|| See above, p. 280. 

f Loc. cit., p. 395 et seq. 



ON COLOURS IN METAL GLASSES, ETC. 283 

transparent and tending to shrink during the process.* Thus a silver leaf which 
before heating was opaque, or only able to transmit deep blue light, and that very 
feebly, was so altered by heating that the light of a candle could be seen through 
forty thicknesses.! But in every case the original colour of the leaf, whether of gold 
or of silver, returns when the leaf is subjected to pressure. 

The differences between the effect of heat on chemically prepared films and on 
beaten leaf correspond to differences between the laminatedf structure of the leaf and 
" the closer and more horn-like texture of the films deposited by chemical agents.''^ 

The optical properties of a laminated metal leaf may be estimated and compared 
with the corresponding properties of an amorphous or granular film of the same metal, 
if the optical constants of a plate built up of a number of flat spheroids with their 
polar axes normal to the plate can be calculated. The general problem of the 
transmission of electromagnetic waves by a medium composed of a number of minute 
similar and similarly situated ellipsoids, distributed at random many to a wave-length, 
has now been solved, and it is hoped that the discussion of the optical properties of 
gold and silver leaf, of the change in those properties which is produced by heat, and 
of the relations of metal films (spheroidal, granular, and amorphous) to polarised light, 
may form the subject of a future memoir. 

With these exceptions, namely, the properties peculiar to beaten leaf and the 
relations of metal films to polarised light, all the experimental relations of gold (and 
other metals) to light, which FARADAY described in his Bakerian Lecture have now 
been discussed, and we are led to the conclusion that the phenomena exhibited 
whether by chemically or electrically deposited films, or by particles of gold diffused 
in glass, jelly, or water are due to different groupings of the metal molecules and to 
variations in the mean distance between adjacent molecules, and in no case are they 
due to allotropic modifications of the molecules themselves. 

13. CAREY LEA'S "Allotropic" Silver. 

In the former communication] | it was suggested that CAREY LEA'S "allotropic" 
silver was in reality only finely divided silver, the division being sufficiently fine to 
admit of the films being optically continuous. 11 He advances** two principal arguments 

* Loc. cit., p. 396. 

t FARADAY, loc. cit., p. 399. 

t BEILBY. loc. cit., p. 43. The difference in structure is shown by the fact that while mercury will 
diffuse slowly and uniformly in the compact film, in the leaf thin streams of mercury may be seen shooting 
rapidly in all directions. 

BEILBY (loc. cit., pp. 48 et seq.) has shown that a layer of exceedingly flat spheroids is generally found 
on the surface of a metal. 

|| 'Phil. Trans.,' A, 1904, p. 419. 

U It is not necessary to suppose the microstructure of the finely divided silver to be granular, as was 
done in the former paper. It may be in part granular and in part amorphous. 

** Fide ' Amer. Journal of Science,' 1889, and 'British Journal of Photography,' March, 1901. Also 
'Phil. Mag.,' vols. 31, 32 (1891). 

2 O 2 



284 MR- J - C. MAXWELL GARNETT 

for the allotropy of silver in the form in which he prepared the metal. We proceed 
to examine these arguments. 

In the first place, then, all CAREY LEA'S silver films were prepared from silver 
suspensions. He claims that these suspensions were "true solutions," and that the 
ability of the silver to remain in solution in water was evidence that the molecules of 
the silver in question differed from those of normal silver, or, in other words, the 
silver was in an allotropic form. We are now, however, familiar with the fact that 
particles of normal silver, as of many other metals, are able, in consequence of mutual 
electrostatic repulsions,* to keep themselves in suspension in quite pure water. 
Again, we have seen that, when a silver solution is prepared by BREDIG'S method, its 
refractive index is that which is possessed by a suspension of small spheres, but not 
of molecules, of silver in water, f and in the same case there is a strong absorption 
band at exactly that point of the spectrum at which small spheres, but not molecules, 
of silver in water would produce a maximum ;J so that in this case the greater part 
of the silver is certainly present in the form of small spheres. Further, if, when 
prepared by deflagration, silver in suspension in water takes the small sphere form, it 
is primd facie probable that it does the same when obtained by CAREY LEA'S 
method, and this probability is increased by the fact that CAREY LEA'S silver 
suspensions exhibited the same red, yellowish-red, and yellow colours which are 
shown by BREDIG'S suspensions of different densities. 

We conclude that CAREY LEA'S " solutions of allotropic silver " consisted of small 
spheres of normal silver in suspension. || 

We should therefore expect that the films obtained by CAREY LEA would be 
similar in constitution and behaviour to BEILBY'S " gold paint " filmsH and to 
FARADAY'S phosphorous films.** This leads us to CAREY LEA'S second argument for 
the allotropy of his silver ; he states : 

"The brittleness of the substances B and C [blue and gold coloured respectively, by reflected light], the 
facility with which they can be reduced to the finest powder makes a striking point of difference between 
allotropic and normal silver. It is probable that normal silver, precipitated in fine powder and set aside 
moist to dry gradually may cohere into brittle lumps, but there would be mere aggregations of discontinuous 
material. With allotropic silver the case is very different, the particles dry in optical contact with each 
other, the surfaces are brilliant, and the material evidently continuous. That this should be brittle 
indicates a totally different state of molecular constitution from that of normal silver." ft 

* See footnote p. 253 above, 
t See above, p. 258. 
t See above, p. 257. 
Above p. 259. 

Cf. also the fact that the silver in a silver-stained glass is in the form of small spheres. 
|| Cf. also evidence given on p. 259 above. 
H See above, p. 279. 

** See above, p. 281. This expectation is verified by a further examination of WOOD'S films. See note 
above p. 282. 

tt 'Brit. Jour. Phot.,' March 1901, p. 21. 



ON COLOURS IN METAL GLASSES, ETC. 285 

All these properties are shared by FARADAY'S " phosphorous " gold,* so that our 
expectation is, so far, fulfilled. We are, in fact, perfectly familiar with " mere 
aggregations of discontinuous material " which are optically continuous for example, 
gold ruby glass. 

Many of the observations which CAREY LEA has recorded on the colours of his 
silver films are in accordance with the expectation that these films, like BEILBY'S 
gold films and FARADAY'S " phosphorous " gold, should behave according to the laws 
(a), (6), and (c) stated above. But two difficulties arise in the way of this 
accordance, for, in the first place CAREY LEA'S recorded observations do not 
sufficiently distinguish between transmitted and reflected light. For example he 
recordst that his freely precipitated silver dissolves to a blood-red colour, and 
proceeds 

"When the substance is brushed over paper and dried rapidly it exhibits a beautiful succession of 
colours. At the moment of applying it it appears blood red| ; when half dry it has a splendid blue colour 
and lustrous metallic reflection;! when quite dry this metallic effect disappears and the colour is matt 
blue."|| 

Lastly, in the case of the films discussed in 11 above, the colour depended on the 
fact that the density of the film was less than that of the metal composing the film 
when in its normal state ; but pressure increased the density to its normal value, at 
the same time bringing out the normal colour, both by reflected and by transmitted 
light, of the metal. And CAREY LEA'S silvers " show a lower specific gravity than 
that of normal silver ; "1 and pressure "instantly converted gold-coloured allotropic 
silver into normal silver."** 

We conclude from the above evidence that this silver was not " allotropic," but 
consisted of normal silver in a finely divided state. 

14. HERMANN VOGEL'S Silver. 
Before leaving the consideration of these discontinuous forms of silver, reference 

O 

must be made to a paper by HERMANN VoGEL,tt in which the author describes how 

* " The least touch of the finger removed the film of gold. . . . These films, though they are certainly 
porous to gas .... have evident optical continuity " (FARADAY, loc. cit., p. 439). Of. also the facts that 
films analogous to CABBY LEA'S did not conduct (BARUS and SCHNEIDER, loc. cit., p. 285), and that the 
phosphorous films did not sensibly conduct electricity (FARADAY, loc. cit., p. 407). 

t 'Brit. Journ. Phot.,' March, 1901, p. 19. 

\ This is the colour by transmitted light when /* is fairly small. Cf. figs. 9 and 11. 

This is the reflected colour for values of p from zero to nearly - 8. Cf. fig. 13. 

|| Professor R. W. WOOD repeated this experiment, using glass instead of paper to support the silver 
film. The metallic effect, then, does not disappear, but remains after the film has become quite dry. 
Cf. above, p. 282. 

H 'Brit. Journ. Phot.,' March, 1901, p. 21. 
** 'Phil. Mag.,' vol. 31, p. 244, 1891. 
tt 'Pogg. Ann.,' CXVIL, p. 316, 1861. 



286 MR, J. C. MAXWELL GARNETT 

he prepared silver of less specific gravity than that of normal silver, by depositing 
that metal on the platinum electrode of a platinum-zinc battery. He also prepared 
silver in suspension in water by chemical means, observing the characteristic amber 
colour and noticing that precipitation could be accelerated by the addition of salt to 
the water. 

VOGEL concludes (loc. cit., p. 337) that there are three forms of silver, (1) regular 
dendritic silver [crystalline] ; (2) granular powdery silver [small spheres] ; (3) mirror 
silver [amorphous]. He found that the second type " tended to the formation of a 
coloured powder," but could be changed into the third type by pressure. He adds 
(loc. cit., p. 441) that the silver precipitated by photography is of the second type, 
and this is the view suggested in the preceding memoir (p. 417), because of the red- 
brown transmitted colour and the green colour of the reflection from fogged photo- 
graphic films, which, according to the analysis given above, 10, are the colours 
exhibited by films of amorphous or granular silver,* of less than standard density. 

15. Allotropic Forms of Metal. 

In the course of the preceding investigations we have been led to recognise that 
variation of the relative position of the molecules of a metal will cause the metal to 
change colour, whether it be examined by reflected or by transmitted light. It has 
been shown, for example, that mere variation in density causes gold in one state to 
transmit green light, in another blue, in another purple, and, in another again, ruby. 
Further, this discovery has led us to the conclusionf that, in order to account for the 
properties of CAREY LEA'S anomalous silvers, it is not necessary to assume the 
existence of an " allotropic " molecule of silver. The question thus arises : Are there 
any other cases in which an allotropic molecule has been unnecessarily postulated ? 

EGBERTS- AUSTEN^ has collected particulars of a large number of supposed cases of 
allotropic states of metals. We proceed to the examination of these particulars in 
order to determine whether the effects, for the explanation of which the allotropic 
molecule was postulated, are not merely those which, according to the analysis of 
10 above, would be due to a decrease in the density of the metal in a granular or 
amorphous state. 

In the first place, then, the discovery that metals in different states, corresponding 
to different methods of preparation, possessed different densities and had widely 
different properties, although chemical analysis could detect no change in the 

* Cf. figs. 9, 11 and 13, and also p. 282 above, where the same colours, exhibited by one of E. W. WOOD'S 
silver films, are discussed. 

t Above, p. 285. 

J ' Metallurgy,' pp. 87 el seq. 

ROBERTS- AUSTEN defines "allotropy" as follows (loc. cit., p. 89): "The occurrence of elements in 
.... allotropic states means that .... the atoms are differently arranged in the molecules." 



ON COLOURS IN METAL OLASSES, ETC. 287 

composition,* does not require those different states to have been allotropic. Again, 
it is unnecessary to suppose that BOLLEY'S lead,t prepared by electrolysis, and similar 
in composition to sheet-lead, is allotropic because it oxidises rapidly in air while sheet- 
lead does not : for the electrolysis gives the essential fine division, and the consequent 
large amount of surface exposed to the air greatly accelerates oxidation. 

Lastly, SCHUTZENBERGER| supposed that the copper deposited on the platinum 
electrode of a copper- platinum cell was allotropic because it was very fragile, its 
density was only about '9 of that of normal copper, it oxidised rapidly in air, and it 
could be converted into normal copper by prolonged contact with dilute sulphuric acid. 
Here, too, the supposition of allotropy is not required to account for the facts. For 
the low density, the fragility and the rapid oxidation are all accounted for by the 
loose structure which we should expect in such a deposit of copper, while CAREY LEA 
found that his silvers, which, if our conclusion at p. 285 is correct, were only finely 
divided silver, could be transformed to normal silver by contact with sulphuric acid. 
Similar remarks apply to SCHUTZENBERGER'S silver.^ 

Consider now MATTHIESSEN'S important generalisation^ that metals may sustain 
change in their molecular condition by union with each other in a fused state. 
ROBERTS- AUSTEN points out|| that the evidence that metals ever assume allotropic 
states, when they enter into union with each other, is difficult to obtain. When 
obtained, the evidence is generally composed of the facts that the specific gravity of 
the normal metal is greater than that of the metal in the state alleged to be allotropic ; 
that the chemical activity is less in amount, although the same in kind, for the former 
than for the latter state ; and that the appearance of the metal is different in the two 
states. Reference is also sometimes made to a difference in physical properties which 
is accounted for by lack of continuity, and consequently of electric conductivity, in 
the supposed allotropic state. IT Occasional reference is also made to a readiness to 
form hydrates which the metal in the latter state exhibits. Setting this last property 
aside, as not yet established, the remaining evidence is not conclusive, for all the facts 
in question are also characteristic of optically continuous granular (or amorphous) 
pieces of metal. Increase of chemical activity, for example, is a consequence of the 
enormous effective surface in a medium built up of independent granules. 

Further, when one metal is united with another in a fused state, a chemical 
compound is not, in general, formed, but the molecules of the two metals freely mix. 
Thus one metal is in solution in the other. So long, therefore, as the temperature 
remains sufficiently high to permit the molecules to move about freely, the molecules 
of each metal tend to segregate, and to group themselves into separate crystals as the 
* JOULE and LYON PLAYFAIR, 'Memoirs of the Chem. Soc.,' vol. iii., p. 57 (1846). 

t EOBERTS-AUSTEN, loc. tit., p. 90. 

J 'Bull. Soc. Chim.,' XXX., p. 3 (1878). 

ROBERTS AUSTEN, loc. cit., p. 87. 

|| Loc. cit., p. 91. 

IF Of. PETERSEN on "Allotropic Forms of Metals" (' Zeitschr. f. Phys. Chem.,' 8, pp. 601, 1891). 



288 MR. J. C. MAXWELL GARNETT ON COLOURS IN METAL GLASSES, ETC. 

temperature is slowly lowered. It is, however, probable that, as in the case of gold 
and copper ruby glasses, the molecules of each metal first group themselves into 
small spheres. If the temperature were rapidly lowered at this stage, this granular 
structure would be fixed in the alloy. If, then, one metal that, suppose, of which 
the larger volume is present were suddenly annihilated, the other metal would 
remain in a granular form, possessing a colour* quite different from that exhibited by 
the normal form of that metal. 

Now when an alloy of potassium and gold containing about 10 per cent, of the 
precious metal is thrown on to water, the potassium is, in effect, annihilated, t and 
the gold is released as a black or dark brown powder. It will be seen from fig. 12 
that granular gold, with a density slightly over '6 of that of normal gold, would 
reflect light of a brown colour, while the reflecting power would not exceed '5. A 
granular structure is thus in accordance with the dull appearance and with the colour 
of the powder. Similarly when a silver-gold alloy containing two parts of silver to 
one of gold is treated with nitric acid the silver is removed, the gold remaining in the 
form of a dull brown powder, which can be converted into bright metallic gold by 
slight pressure or by heating to redness. It appears, therefore, that this brown 
powder is probably granular gold, the component particles being small compared with 
a wavelength of light ; so that, once more, the evidence J does not require us to 
suppose this form of gold to be allotropic. 

Finally, it seems unnecessary to assert that iron released from its amalgam by 
distilling away the mercury is in an allotropic form because it takes fire on exposure 
to the air. For this burning of the iron would be the consequence of the large 
surface exposed to the air by an extremely finely divided form of the metal. 

We conclude, therefore, that in none of the cases of supposed allotropy, which we 
have examined in this section, has the existence of an allotropic form of metal been 
established. 

* See 10 above. 

t Of. ROBERTS-AUSTEN, loc. dt., p. 91. The potassium does not catch fire, but combines with the water 
to form KHO (which immediately passes into solution and is thus removed) and H which catches fire. 

t We must except that of the alleged formation of auric hydrate, but I have been unable to obtain any 
confirmation of the existence of such a compound. 



VIII. On the Intensity and Direction of the Force of Grarity in India. 

By Lieut.-Colond S. G. BCJRUABD, H.E., F.R.K. 

Received March 30, Read April 13, 1905. 

['PLATES 14-20.] 

(1.) The Pendulum Observations of /.sv/,-7-7'.^. 

BETWEEN 1865 and 1873 observations were taken at 31 stations in India by 
Captains BASEVI and HEAVISIDE with the Royal Society's seconds pendulums. 
The results were published in Vol. V. of the ' Account of the Operations of the 
Great Trigonometrical Survey of India,' and have been subsequently discussed by 
many authorities.* 

Captain BASEVI expressed his results in terms of N, the number of vibrations of 
the mean pendulum observed in a mean solar day. The International Geodetic 
Association show their results in dynes, and it is desirable that we should follow their 
example. We have, therefore, to change the notation employed by our predecessors. 

The fundamental formula, expressing the relation between the length of a 
pendulum, its time of vibration and the accelerating force g, is t = TT \/(l/g)- If N be 
the number of vibrations, which a pendulum of length / makes in a mean solar day of 
86,400 mean time seconds, then 

M _ 86400 _ 86400 /g 

T~ ~ \f 1 ' 

v 77" r ' 

where t is the time of vibration. 

If N becomes N + c/N, when g becomes g + dg, then 



> 

By this formula, if certain values of N and g be adopted for a Standard Station, 
the results of the older pendulum observations can be converted, and the symbol g 
substituted for N.t 

The pendulum observations in India were undertaken, and are now being extended, 
with the object of determining the difference between the force of gravity as observed 

* See 'Phil. Trans.,' A, vol. 186, 1895; HELMERT'S 'Die Schwerkraft im Hochgebirge ' ; HELMERT'S 
'Hdhere Geodiisie'; CLARKE'S 'Geodesy'; FISHER'S 'Physics of the Earth's Crust.' 
t dg = 0'0226(/N is a rough rule, sufficiently accurate for many purposes. 
VOL. CCV. A 394. 2 P 12.10.05 



290 



LIEUT.-COLONEL S. G. BURRARD ON THE 



at the standard stations of Europe and as observed in India ; the determination of the 
absolute value of the force of gravity did not and does not form any part of the 
operations. 

The values of gravity exhibited in Table I. are taken from Professor HELMERT'S 
Report to the International Geodetic Conference, which was held at Paris in 1900. 

TABLE I. -BASEVI'S and HEAVISIDE'S Results Expressed in Dynes. 





Station. Latitude. 


Longitude. 



I 

3 

E 


Observed value. 


Correction for unevenness 
of ground. 


i 

0-*. 

II 

i 

+ 
^ 


<7 attraction of the mass 
above sea-level = g a ". 


Tlleoretical value. 


- 

I 

"* 


A 

1 
ft 








Metres. 


.'/ 
eentims. 


3' -9- 


eentims. 


eentims. 


Yo 
eentims. 


eentims. 


eentims. 




/ 

Punnae .... . . . ' + 8 9 '5 


+ 77 37'- 7 


15 


978 -095 


000 


978-100 


978-098 


978*105 


-0*007 


-0*005 






+ 77 41 '5 


51 


978 *090 





978-108 


978-100 


978*105 


5 


+ 1 






+ 73 '0 


2 


978 '191 





978-192 


978-191 


978*108 


+ 83 


-r 84 


<J 




+ 76 17 '6 


2 


978 !> 





978-167 


978-166 


978-141 


+ 25 


+ 26 


o 


Mangalore +12 51 '6 


+ 74 49*6 


8 


978-231 
978 '237 






978-235 
978 -239 


978 -234 
978 -239 


978 -257 

978*266 


- 23 
- 27 


- 22 
- 27 








3 


978 '4 17 




978 "448 


978-447 


978*441 


+ 6 


+ 7 




Colaba Observatory (Bombay) . . +13 53 -8 


+ 72 48-8 


11 


978-605 





978-608 


978-607 


978 *545 


+ 62 


+ 63 




Mallapatti + 9 28 '8 
Pachapaliam . +10 59 '7 


+ 78 O-H 
+ 77 37 '5 


88 
296 


978 -091 
978 -084 






978-118 
978-175 


978-108 
978-140 


978*141 
978 *189 


- 33 

- 49 


- 23 
- 14 




Bangalore South . . + 13 '7 


+ 77 35 '1 


950 


977-998 





978 -289 


978-179 


978*263 


84 


+ 2 




Bangalore, North + 13 4 '9 
Namthab&l . . . . . +15 5 '9 


+ 77 39-3 
+ 77 36 '5 


917 
358 


978 -018 
978 -"07 







978-299 
978-318 


978 -193 
978 '275 


978*266 
978 -352 


- H 


+ at 

- 34 






+ 77 38 '5 


584 


978 '213 





978*461 


978 '394 


978-451 


"7 


+ 10 




Damargiila +18 3 '3 


+ 77 40'1 


593 


978 -283 





978'484 


978-396 


978-499 


- 103 


- 35 








522 


Q78 -402 




978 '563 


978 "502 


978 -555 


53 


-r 8 


i 






342 


978 "539 


o 


978'642 


978 (3 


978*651 


48 


9 


M 


Cak-utta, Survey Office .... +22 32 '9 


+ 33 21T> 
+ 77 40 '9 


6 

516 


978 -776 
978 "674 



+ 2 


978-778 
978 "832 


978-777 
978*774 


978*764 
978 *833 


+ 13 
59 


+ 14 
- 1 








538 


478-7* 3 '{ 








978*867 


42 


+ 21 
















978*835 




88 


30 




Usira + 26 57 -1 
Datairi + ''8 44'1 


+ 77 37'9 


247 
* J 18 


978-972 
q;q -QQ5 


+ I 


979 "048 


979-021 
979-137 


979*067 
979*200 


- 46 
63 


- 19 
38 




Kalh'tna + 29 30*9 


+ 77 T-t'2 


247 


979-107 


I 




979*154 


979*260 


106 


77 




Nojli . . +29 53 '5 




269 


979-110 


o 


979-198 


979-167 


979*290 


123 


92 




Meean Meer . . +31 31 & 


+ 74 23 '3 


>15 


979 -273 




979 -339 


979*314 


979 *420 


108 


81 
























is 


Dehra Dun Observatory .... + 30 19'5 


+ 78 3-3 
+ 78 4*4 


683 
2109 


978 -962 
978 '751 


+ 7 
+ 27 


979-172 


979*100 
979*181 


979*324 
979*335 


- 224 
154 


- 152 
+ 65 


X*' 


More +33 ljj'7 


+ 77 52*0 


46% 


978-137 


+ 9 


979*580 


979 *044 


979 *562 


518 


*. 18 

























EXPLANATION OP SYMBOLS EMPLOYED. 
For fuller details as to the manner in whirl* these numbers are derived, see the explanation of Table II. 

/ 2H\ /H + R\ 2 

?V' + ~K I ''ppresonts g \ % / ; the third place of decimals in expressions for gravity at high stations may differ by two or 

three units according to the form of the formula used. 

g = the value of the force of gravity as observed at the height H, the value at Kew being assumed 981 -200. 
g' = the observed value of gravity reduced to an infinite horizontal plain of height H. 
g' - g = topographical correction due to the irregular distribution of mass in the vicinity of the station. 
g a = the observed value of gravity reduced to sea-level for height only. 

g a " = the observed value of gravity reduced to sea-level both for height and for mass above sea-level. 

y = the theoretical value of gravity computed from HKLMERT'S formula of 1884, namely, 978 -000 eentims. (1 + -005310 sin" (>). 
9o" - Yo = load variation of gravity from the normal, as computed by BOUQUKR, and as used for the determination of mountain-compensation. 
?o - Yo = 'oca' variation of gravity, as used by HELMKST in his determination of the Figure of the Garth. 



INTENSITY AND DIRECTION OF THE FORCE OF GRAVITY IN INDIA. 291 

The differences between the observed and computed values in Table I. correspond 
very nearly to the differences between the observed and computed values of N, as 
formerly given by General WALKEK. That the correspondence is not exact is due to 
the adoption by HELMERT and WALKEK of different constants in CLAIRAUT'S law. 

The physical meaning of BASEVI'S pendulum results was for many years the subject 
of controversy.* The deficiency of gravity which he had found to exist in Himalayan 
regions was attributed by some authorities to the elevation of the level surface above 
the surface of the mean spheroid, and by others to the defective density of the under- 
lying crust; by the former the surface of the geoid was held to depart largely in 
certain places from that of the spheroid, and by the latter the two surfaces were 
assumed to be almost identical. In his ' Schwerkraft im Hochgebirge,' published in 
1890, Professor HELMERT gave a mathematical solution of the problem, and his 
writings have closed the controversy. 

A graphical interpretation of the results of Table I. is given in Plate 14, the method 
by which the several ordinates are computed being explained in Table II. below. The 
first figure of the Plate shows the height above sea-level, as determined by spirit 
levelling, of the surface of India along its central meridian. The second figure shows 
the deficiency of matter in the underlying crust, as deduced from BASEVI'S pendulum 
results. The third figure gives the differences between the ordinates in the two 
upper figures, and shows the surface of India as it would be if the crust were 
everywhere of equal density. An examination of the figures of this Plate brings to 
light four significant facts : 

(1) That there exists in the earth's crust throughout India a general deficiency 

of matter as compared to Europe ; t 

(2) That the apparent excess of matter above sea-level, which the eye observes 

at More (Station 43) under the form of mountains, is largely compensated 
by subjacent deficiencies ; 

(3) That an extraordinary deficiency of matter underlies the stations of Dehra 

Dun, Kaliana and Nojli (Nos. 38, 37, 36), stations situated not in the 
Himalayas, like Mussooree (No. 41), but in the plains at the foot of 
the Himalayas ; this deficiency leads one to beliere that the pressure 
of the Himalaya Mountains upon the crust is diminishing the density of 
the latter under the surrounding plains ; 

(4) If we disregard the evidence of fig. 1, and if we consider only the distribution 

of mass in the surrounding crust, we see that stations in the plains of 

* See preface to Vol. V. of ' Account of Operations of the Great Trigonometrical Survey of India.' 

t The peninsula of India is composed of crystalline and volcanic rocks ; the great age of the former and 

the great weight of the latter would lead us to expect a high value for g ; that g should be abnormally 

small is, from a geological point of view, surprising. 

2 P 2 



292 LIEUT.-COLONEL S. G. BURRARD ON THE 

Northern India, such as Nos. 36 and 37, are situated in a deep wide 
valley between two ranges of mountains, one of which, the Himalayan, is 
visible, the other, with its summit at Station 24, invisible.* 

The northern end of the section in Hg. 3 conveys the idea that the Himalayan 
mass is pressing upon the crust and producing a dimple, such as that described in 
Chapter VII. of Professor GKOIWSK DARWIN'S work on 'Tides and Kindred 
Phenomena.' 

The sections given in tigs. 2 and 3 of Plate 14 are based on Professor HKLMERT'S 
condensation theory and have been constructed by means of his formulas from the 
data in Table II. The numbers of the stations are not continuous, because pendulum 
observations were not taken at all the astronomical stations. 

After 1874 no pendulum observations were taken in India, but the deflection of the 
plumb-line continued to be determined in different parts of the country. By the 
year 1900 the astronomical latitude of 159 stations, the astronomical azimuth at 209, 
and the amplitude of 55 arcs of longitude had been observed, and thus a large amount 
of evidence relating to the direction of gravity had accumulated. A discussion of the 
datal; then available showed that it would be desirable to associate determinations of 
the intensity of the force of gravity with observations of the plumb-line, and in 1902 
the Indian Government sanctioned the re-opening of pendulum observations and the 
purchase of a new apparatus of VON STERNECK'S pattern. 

(2.) Tin 1 Pendulnin Observations of 1003-04. 

The new apparatus was standardised at Kew and Greenwich in the autumn of 
1903, and was taken to India by Major LENOX CONYNGHAM in November of that 
year. Upon its arrival he thought it advisable to commence work at some of 
BASEVI'S stations. The accuracy of BASEVI'S results, as given in Tables I. and II., 
had been questioned by Professor HELMERT in his report to the International 
Geodetic Conference of 1900. It had been there pointed out that the observer had 
had no means of measuring the flexure of the pendulum stand, that during his 
standardisation at Kew his pendulums had not been supported on the stand 
subsequently used in India but between a stone pillar and a wall, and that when he 
visited the high Himalayan station of More he had substituted a light portable stand 
for that belonging to the Royal Society's apparatus. 

* Fig. 1 of Plate 14 shows that the altitude of Station 38 above sea-level is 145 metres greater than that 
of Station 24; fig. 3 shows that if the underlying crust were brought to a uniform density of 2-8 the 
altitude of Station 38 would be 1430 metres less than that of Station 24. The visible fall of nearly 
500 feet from Station 38 to Station 24 is converted by the pendulum diagrams into a rise of nearly 
4*700 feet. 

t 'Professional Papers of the Survey of India,' No. 5 of 1902. "The Attraction of the Himalaya 
Mountains upon the Plumb-line in India," 



INTENSITY AND DIRECTION OF THE FORCE OF GRAVITY IN INDIA. 293 



TABLE II. 









u 


S 






Hal 

-3. 5 


11 


Station. 


Latitude. 


11*5 


5 - 
5 






._ Q ^..._ .. 


a 






Millinis. 


i 


Punnap 


/ 

8 9 '5 







Kudankolain . . . 


M Kl-4 


1 


4 


Mallapatti. . . . 


9 29 '0 


108 


5 


Pachai>aliain . . . 


10 59-7 


227 


1) 


Bangalore, South . 


13 0-7 


388 


7 


Bangalore, North . 


13 4-9 


391 


10 


Namthabad . . . 


15 5 -II 


555 


12 


Kodangal .... 


17 8'0 


718 


13 


Damargida . . . 


18 3-3 


791 


15 


Somtana .... 


HI 5-0 


874 


17 


Badgaon .... 


2ll 4I'I 


1006 


20 


Ahmadpur. . . . 


23 36-4 


1238 


21 


Kalianpur .... 


21 7'2 


1276 


29 
31 


PahArgarh. , . . 


24 56'1 


1342 
1503 




Datairi 


28 4 1 ' 1 


16(6 


38 




29 30 '9 


17O9 


37 


Nojli . . . 


29 53 '5 




38 


Dehra Dun . . . 


30 HI '5 


1771 


41 
43 


Mussooree. . . . 
More 


30 27'7 

:t3 15 -7 


1 783 
2008 











+3 1) 


S-J 


l| M_.| 


11 -D. 


j H = Hei 
^ ' above sea- 

1 i 


II to scale 
ill millims. 

0-1 


3 i :1 ~ta 
'-- a! ~^ 

M < 1 -- ",nii!i 




Metres. 


To scale in 
millims. 
for fig. 3. 


15 


7 +61 + 0-5 


- 46 


- o-l 


51 


n -1 


5 + 43 + H '3 


+ 8 


+ o-l 


88 


0'7 


:13 + 2xi| + 2 '3 


- 1118 


- 1'6 


29fl 


2'1 


- 49 + 121 + 3'l 


- I2 


- I'd 


950 


7-6 


-84 + 727 + 5'8 


+ 223 


f 1 '8 


917 


7-3 


- 73 + 032 + 5-1 


+ 2X3 


+ 2 '2 


355 


2-11 


- 77 + 6H7 + 5-3 


- 3011 


- 2-1 


581 


4'7 


- 57 + 193 + 311 


+ HI 


+ II 'S 


5113 


4'8 


- Iii3 + S02 +7M 


- 2911 


- 2-3 


522 


1 '2 


- 53 + 159 + 3 '7 


4- l'3 


-f n "5 


312 


2'7 


- 48 + 111. + 3-3 


- 71 


- M 'H 


516 


I'l 


- 511 -f 511 + I'll 


-t- 5 


+ ii'l 


538 


4 '3 


12 + 361 -I- 2-H 


+ 171 


+ 1-1 


500 


4'0 


- 88 + 762 + 6-1 


- 2li2 - 2-1 


217 


2-0 - 46 + 398 1- 3'2 


- 151 - 1 -2 


218 


1-8 - 63 + 515 + I'l 


- 327 , - 2'6 


217 


2'll - lilt. H- HIS + 7'3 


- 671 - 5'3 


261) 


2'1 - 123 + 1(165 + 8-5 


- 7H6 


- 'l 


883 


5-5 - 221 + 19311 + 13-3 


-1256 


- lil'O 


2109 


16-9 - 154 + 1333 4- 10-7 


+ 876 


+ 6 '2 


469H 


37 '6 


- 318 1 + 4484 ; + 3.V9 

1 


+ 212 


+ 1'7 

l 



EXPLANATION OF TABLE II. 

Given the amount of matter in tlie crust at a stauJaril station, we wish to find from pendulum observations, the excess or deficiency of matter 
underlying any other station ; from observation we find ilrj, the local variation of gravity from the normal, and we wish to determine the mass 
whose attraction at sea-level is equivalent to dg. From its attraction only we cannot determine both the height and density of a hidden mass, 
but If we assume that the density is equal to 2 '8, the normal density of surface rocks, we can then ascertain the height; by this assumption we. 
mean that the density of a hidden disturbing mass is 2 -S in excess of the normal density of the surrounding crust . The problem to lie solved is, 
therefore : given a small attraction dij, what is the height of the attracting mass, its density being 2-8? 

It is necessary to consider how dij is obtained ; by observations taken at a station of height H we find the value of gravity to IK; y. To oblain 
the corresponding value of gravity at sea-level, <7 , we have firstly to correct for the amount H, by which the distance of the station from the 

centre of the earth exceeds the earth's radius, 2l' = 

fj 



R- 



= ij (\ + \. 
\ R / 



This correction would be sufficient if the obser\ ing station were in mid-air and over the wean, but when we observe at a station on land, wr 
have to consider the attraction of that portion of the crust that lies between sea-level and the station ; this attraction tends to increase Un- 
observed value of g, and the correction for it is ncgat ive. The attraction of a horizontal plateau of height H and density S upon a pendulum 
situated at the centre of its upper surface is A = 2*611. The force of gravity at sea-level is g = JirRA, where A is the mean density of the earth. 



Then if y a " be the value of gravity at sea-level corrected Iwth for height of station and for the attraction of the intervening mass, we get the 

well-known formula of UOUGUEK, y a " = y a A = ij ( 1 + - ^-|f ). (/" gives then the obsen-eit value of gravity at an ideal station, situated upon 

\ R 4 K / 

a continent, whose surface is level with the sea. 
Now <tg = g a " fa, where / is the theoretical value of gravity. To lind the height of a plateau whose attraction would be sufficient to 

increase the observed force of gravity by 0-001 centim., we have . . y = dg = O'OOl. II = O'OOl x ; x . Assuming the earth txi be a 

4 K y 

sphere with a mean radius of 6367000 metres, and the mean value of the force of gravity to lie 980-0, we get II = O'OOl x J x ** l( _ _ = S'S573 metres. 

The attraction thus of a plateau of height 8 '6373 metres wilt increase the observed value of gravity by O'OOl, and vice versa ; if the observed value 
of gravity at sea-level differs from the theoretical value by -t-'O'OOl there is an excess of matter in the underlying crust equal to a disc 8 '6573 
metres thick of a density 2 '8. 

If we imagine that from the surface to a depth 1), the density of the crust underlying the station is less by 2 '8 than the normal surface 
density, then D = - (#," - yj 8 '8573 metres. The visible excess of matter will be equal to H (see fig. 1), the hidden deficiency will be equal to D 
(see fig. 2), and the actual disturbing mass, shown in the section of fig. 3, will be (H D). 

Prom Table II. it appears that at MorA the value of g a " is '518 less than y ; therefore the hidden deficiency = D = 518 x 8 '573 = 4484 metres 
(fig. 2). The height of the visible mountain at Mor6 is H = 4696 (fig. 1) ; the actual excess of matter in the crust at More = (H - D) = 212 
metres (fig. 3). 

At Dehra Dun <y " - y u > = - 0'224, hidden deficiency = D = 224 x 8-8573 = 1939 metres (fig. 2). The altitude of Dehra Dun is S3 metres 
(fig. 1) ; at this station, then, the hidden deficiency exceeds the visible excess, and the resultant is (H - D) = 683 - 1939 = - 1256 metres (fig. 3). 

At the important station of Kalianpur (</" y a ) = '042, the hidden deficiency = D = 42 x 8 '6573 = 364 metres, the visible excess at 
Kalianpur = H = 538 metres. There exists, therefore, at Kali:in pur a resultant excess of matter in the crust equal to a disc of density 2 '8, and 
pf height 174 metres. The existence of this excess has been questioned, and the calculation is therefore giren in detail. 



294 



LIEUT.-COLONEL S. G. BUERAED ON THE 



From the results of observations taken by Austrian observers at some of the coast 
stations, Professor HELMERT had arrived at the conclusion that BASEVI'S values 
required a correction of +0'047.* The importance of such a correction cannot be 
overestimated ; it would have indeed the effect of largely neutralising the negative 
character of the values of (.(/" y tl ) and of (H D) in Tables I. and II., and it would 
render the value of (#o" yo) f r our standard station of Kalidnpur actually positive. 
Such a correction would lower the line of sea-level as drawn on figs. 2 and 3 of 
Plate 1 4, but would not otherwise affect the sections in these figures. 

Major LENOX CONYNGHAM' s first station in India was Dehra Dun; his results 
there were astonishing, for they showed that BASEVI'S value was no less than 
0'103 centim. too small. t LKNOX CONYNGHAM then visited Calcutta, Bombay, 
Madras, and Mussooree. At Calcutta observations were rendered impossible by the 
ceaseless vibrations of the ground, which proved sufficient to cause the pendulums, if 
left suspended at rest, to oscillate visibly in a few minutes ; this effect on the 
pendulums was produced in whatever plane the latter were swung. LENOX 
CONYNGHAM had therefore to abandon Calcutta without obtaining any results ; that 
lie failed where BASEVI had succeeded was probably 'due to the half-seconds 
pendulums of the new apparatus being more affected by earth-vibrations than the old 
seconds pendulums. 

* The correction for More was indeterminate, but probably larger than 0-047, owing to the lightness of 
the stand employed. 

t This extraordinary difference could only mean that BASEVI'S final value of N was too small by 
4 whole seconds of time. BASEVI'S observations at Dehra Dun lasted four months, and included 234 
independent sets of swings taken at pressures varying from half-an-inch to 28 inches, and at temperatures 
varying from 48 to 102" Fahrenheit. 





H. 


9- 


BASEVI'S 1st determination 


seconds 
86,021 '38 
86,020 '74 


centiins. 
978 -973 
978 -959 


2nd 


Weighted mean 


86,020 -86 


978 -962 


LENOX CONYNGHAM in January, 1904 




979 -063 
979-066 


June, 1904 . . . . . . 


Mean 




! 


979-065 




i 


Difference between BASEVI'S two determinations =0 '014 centiin. 
LENOX CONYNGHAM'S two determinations =0 '003 
BASETI and LENOX CONTNGHAM =0 '103 centim. 


centim. 



INTENSITY AND DIRECTION OF THE FORCE OF GRAVITY IN INDIA. 295 



THE Force of Gravity in Dynes as observed by 





BASEVI and HEAVISIDE 
in 1866-73. 


LENOX CONYNGHAM 

in 1904. 


Difference. 


Dehra Dun . 


centims. 

978-962 


centims. 

979-065 


centims. 

+ 0-103 


Madras ... 


978-237 


978-281 


+ ' 044 


Bombay .... 


978-605 


978-632 


+ 0-027 


Mussooree 


978-751 


978-795 


+ 0-044 











LENOX CONYNGHAM'S observations confirm Professor HELMERT'S prediction that 
BASEVI and HEAVISIDE'S results would be found too small. The sections in figs. 2 
and 3 of Plate 14 of this paper have been based on their results, and it may be asked 
what purpose has been served by the construction of sections from impugned data ? 
The answer to this question is that BASEVI'S results have been accepted by geodesists 
and have formed the basis of controversies and theories ; they have, too, been 
rendered historic by the difficulties and death of the observer at More", and by the 
great light they undoubtedly threw upon Himalayan formation. Now that pendulum 
observations are being re-opened, I have thought it advisable in an historical 
retrospect to give a graphical summary of the results that were formerly obtained, 
and that have so profoundly influenced the ideas of geodesists. 

In figs. 2 and 3 the deficiency underlying Dehra Dun (38) will be reduced by 
almost one-half if LENOX CONYNGHAM'S value be substituted for BASEVI'S. Similarly 
the height of Mussooree (41) in fig. 3 will be almost doubled. 

In the near future BASEVI'S other stations will possibly be visited ; it seems certain 
that his results will everywhere be found too small, that throughout fig. 2 the curve 
of deficiency will have to be raised, and that in fig. 3 the line of sea-level will have to 
be lowered. 

From LENOX CONYNGHAM'S observations at Bombay and Dehra Dim, it appears 
that BASEVI'S and HEAVISIDE'S results are not in error by any constant quantity, and 
that the error of each will have to be separately determined ; it is not easy to account 
for the variation in the magnitudes of their errors ; their observations were taken 
with a care that it is difficult for us to equal ; in assuming that flexure could be 
prevented by the employment of a rigid stand, the old observers were following the 
highest authorities of their time ; the only faults that have been found with their 
work are such as would tend to produce constant error. That their errors vary so 
largely can only, I think, be explained on the supposition that the flexure of the 
wooden stand of the Eoyal Society's apparatus was influenced by temperature and 
humidity. 

The idea that gravity is exceptionally weak throughout India as compared to 



296 LIEUT. -COLONEL S. G. BURRARD ON THE 

Europe can no longer be upheld ;* the so-called " marked negative variation" of many 
writers has been found to rest on erroneous data. 

The theory of the compensation of the Himalayas has been based to a large extent 
on the old pendulum results at Mussooree and More". The sections in figs. 2 and 3 
show that a hidden deficiency of matter underlies the station of Mussooree (41) 
equivalent to about three-fifths of the visible excess ; LENOX CONYNGHAM'S recent 
result reduces this hidden deficiency to one-third only of the visible excess. 

Figs. 2 and 3 might lead to the belief that the Himalayas at More' (43) are almost 
entirely compensated. The height of the visible excess is 4696 metres, the depth of 
the ideal deficiency 4484 metres. But LENOX CONYNGHAM has not visited More, 
and, as BASEVI employed there a special and lighter stand, it is impossible to gauge 
the error introduced into his result by its flexure ; we have lately gained some idea of 
the effects of the flexure of the lloyal Society's heavy stand, and we can only suppose 
that the light More" stand was less rigid. That the Himalayas at More are 
compensated to a considerable extent is certain ; that the error due to flexure could 
have affected BASEVI'S result to the extent of 22 seconds of time is out of the 
question. On the other hand, it is more than probable that the compensation, that 
does exist, lacks that completeness, which has hitherto been considered among its 
most remarkable features.! 

(3.) Deflections of the Plumb-line. 

In 1895 General WALKER published an admirable classification of the deflections of 
the plumb-line that had been observed in India.j His object was to present the data 
in the form of arcs of meridian and parallel for the use of mathematicians investigating 
the values of the earth's axes. 

In 1898 Great Britain joined the International Geodetic Association, and Professor 
GEORGE DARWIN, F.ll.S., was nominated to represent her at International Conferences. 
These steps have brought India into touch with modern European ideas, and have 
shown vis that the aims of geodesy are no longer limited to the measurements of arcs 
of meridian and parallel, and to the determinations of the axes of a mean spheroid. 
At the International Conference, held at Copenhagen in 1903, the following resolution 
was passed : 

" II est desirable qu'on fasse dans les Indes anglaises une etude approfondie de la 
repartition de la pesanteur, tant dans les contrees montagneuses que dans 
les plaines. 

* No standard value of g has as yet been adopted by the International Geodetic Association. When 
the absolute values of gravity at European standard stations have been finally determined, it may be found 
that the values at Kew and Greenwich, which we are now accepting as o'ur standards, are not themselves 
normal. Both BASEVI'S old and LENOX CONYNGHAM'S new values will then have to be corrected by a 
constant quantity. 

t CLARKE'S ' Geodesy,' p. 350. 

| 'Phil. Trans.,' A, vol. 186, 1895. 



INTENSITY AND DIRECTION OF THE FORCE OF GRAVITY IN INDIA. 297 

" Attendu que c'est seulement par cette etude qu'on pourra obtenir une repre"- 
sentation exacte de la distribution des masses dans 1'ecorce terrestre et de la 
forme du ge"oide dans ces contre"es." 

In India itself our view of the subject has been modified by our recent discoveries 
that the direction of gravity is liable to a constant deflection throughout large 
regions, and that the density of the earth's crust may differ constantly from the 
mean surface value throughout great areas. In 1895, when General WALKER'S 
paper was written, it was believed that deflections of the plumb-line were accidental 
and due to small local pockets of exceptional density studding every part of the 
country. It was considered proper to treat deflections by minimum squares,* and it 
was held that the true direction of the normal to the mean figure could be discovered 
by grouping stations round a centre, and by assuming that in the mean of the group 
the effects of local attraction are cancelled. 

There are now grounds for believing that the direction of gravity may be deflected 
through 8 seconds of arc or move over an area of thousands of square miles. To 
assume, therefore, that its mean direction as deduced from a group of contiguous 
stations coincides with the normal, is seen to be hardly more justifiable than to 
assume that the mean direction of the magnetic needle, as observed at several 
stations in Surrey, gives the true direction of north. 

The investigation of the laws governing the deflection of gravity in India has been 
impeded by many difficulties. Political considerations have erected a barrier round 
Nepal and Bhutan, which geodetic operations have been unable to pass. Nepal and 
Bhutan include almost the whole of the central and southern Himalayas. Geodesists 
wish to approach the Himalayas from the south, and, by working gradually towards 
their centre of mass, to discover their influence on the plumb-line. Being excluded 
from Nepal and Bhutan, they have had to attack the mountainous area at its south- 
west salient at Dehra Dun (see Plate 16). 

They have, moreover, been generally confined to deducing the direction of gravity 
from latitude observations, which give only the meridional component. It is true 
that our longitude observations show the direction of gravity in the prime vertical, 
and if we could observe both the latitude and longitude of points on the Himalayan 
snows, it would be possible to calculate the actual direction of gravity from its two 
measured components. But until wireless telegraphy can be utilised for longitude 
determinations, our longitude stations will have to be located near telegraph offices 
instead of on mountain tops. We have observed astronomical azimuths at numerous 
stations and their results will in the future be available for plumb-line discussions, but 

* When arcs of meridian are employed to determine the figure of the mean spheroid they are not 
regarded as fixed in latitude. Their most probable positions in latitude are found by the method of 
minimum squares. Each arc is moved up or down its meridional ellipse until a position is found for it in 
which the squares of the deflections of the plumb-line are a minimum ; by this method large deflections 
may be eliminated that exist in nature. 

VOL, CCV. A. 2 Q 



298 



LIEUT.-COLONEL S. G. BUEEAED ON THE 



the geodetic azimuths are at present affected by the errors accumulated in the tri- 
angulation, which have not as yet been determined. Whilst, then, we are endeavouring 
to discover the influence on the plumb-line of a mountainous mass situated to the north- 
east, we are limited to observations which give the north and south component only. 

The other difficulties attending plumb-line research are, that our deductions are 
based upon an assumed figure of the earth and upon an assumed direction of gravity 
at a station of origin. We have to imagine a mean spheroid, and we then assume 
that the angle of inclination between the surface of this spheroid and the actual level 
surface at any place is equal to the deflection of the plumb-line ; we have also to select 
some station as an origin, and to assume that the surfaces of the spheroid and geoid 
are there parallel. We have finally to decide from the results accumulated over wide 
areas, whether the fundamental assumptions on which those results are based the 
assumptions of spheroid and origin are correct. 

In the publications of the ' Survey of India ' the deflections of the plumb-line have 
been always based (1) on the mean spheroid of EVEREST, and (2) on the assumption 
that gravity acts normally at Kalianpur, our geodetic origin. In his paper on 
' Geodesy,' published in 1895, General WALKER gave the deflections of the plumb- 
line in terms of the spheroid of CLARKE. 

EVEREST'S spheroid had agreed closely with BESSEL'S ; but the objection had been 
raised to both that their values of the ellipticity, 1/300'80 and 1/299'15, differed too 
seriously from the value 1/289 derived by CLAIRATJT'S theorem from pendulum 
observations. In 1880, in his work on ' Geodesy,' Colonel CLARKE deduced an 
ellipticity of 1/293 '4G5 from measures of arcs, and of 1/293 from pendulum results; 
and his removal of the hiatus gave great weight to his spheroid. Professor 
HELMERT'S investigations have, however, shown that modern pendulum work has not 
borne out CLARKE'S result, and that BESSEL'S ellipticity was after all nearer the truth. 

Recent geodetic measurements have tended to confirm the accuracy of CLARKE'S 
value of the major axis, and to indicate that BESSEL'S value was too small.* Until a 
new determination of the dimensions of the mean spheroid has been made under the 
authority of the International Geodetic Association, it is advisable for us to adopt 
for computations a spheroid that has the major axis of CLARKE and the ellipticity of 
BESSEL. 

ELEMENTS of Spheroids. 





Major axis in metres. 


Ellipticity. 


BESSEL 


6 377 397 


1/299-15 


EVEREST .... 


6 377 193 


1/300 '80 


CLARKE . . 


6 378 190 


1 /29V 47 


CLARKE-BESSEL . . . 


6 378 190 


1/299 '15 









'United States Coast and Geodetic Survey.' "The Transcontinental Triangulation, 1900 ;" "The 
Eastern Oblique Arc of the United States," 1901. 



INTENSITY AND DIRECTION OF THE FORCE OF GRAVITY IN INDIA. 299 

In Tables III. and IV., given hereafter, the deflections are shown in terms of the 
Everest, the Clarke, and the Clarke-Bessel spheroids. 

If we compare the deflections of the plumb-line as referred respectively to the 
Everest and Clarke spheroids, we find that the values are almost identical at all 
stations. The agreement between the two series, though very remarkable, is a mere 
coincidence ; the influence of CLARKE'S increased ellipticity happens always in India 
to neutralise the influence of his increased major axis. 

If we employ the Clarke-Bessel spheroid, the deduced deflections of gravity are 
appreciably modified. 

(4.) The Regional Classification of Deflections. 

It was in 1900 that the suggestion was first made that the deflections of gravity 
in India, which had hitherto been attributed to accidental and local attractions, could 
be broadly classified by regions. This new theory had as a working hypothesis an 
advantage over the old in that it could be tested by further investigation in the field. 
From the classification of results of regions it was predicted that a southerly 
deflection of gravity would be found to exist throughout a great zone enclosing the 
main valley of the Ganges and running parallel to the Himalayas for 1000 miles; 
but that both north and south of this zone northerly deflections would be met with 
(vide Plate 15). 

With the object of testing the correctness of these predictions, Lieutenant COWIE, 
R.E., proceeded in 1901 to observe several latitudes between Calcutta and Phallut, 
working across the zone of southerly deflection and up to the Himalayas (vide 
Plate 15). The results which he obtained were as follows: In the country 
immediately south of the zone northerly deflections of 3" and 4" were found ; at 
Calcutta the inclination of gravity was slightly southerly. In the 200 miles 
immediately north of Calcutta, COWIE found southerly deflections at four successive 
stations ; the inclination of gravity then changed to northerly, at Jalpaiguri it was 
6" northerly, at Siliguri 23", at Kurseong 51", and at Phallut 37". 

In 1902-03, Lieutenant COWIE was directed to work again northwards across the 
zone and to follow the meridian of 79. The results which he obtained were as 
follows : In latitude 23 30' the direction of gravity was inclined 5" towards the 
north ; in the next 200 miles Lieutenant COWIE found a southerly deflection at seven 
successive stations ; in latitude 27 47' the inclination of gravity began to be slightly 
northerly; in 29 16' its inclination was 12" northwards. At Birond, in the hills, 
Lieutenant COWIE found a deflection of 44" north. 

It can, therefore, now be prophesied with tolerable certainty that on all Himalayan 
meridians the direction of gravity will be found to follow one general law ; in the 
neighbourhood of the tropic, as we move northwards, its direction will change from 
northerly to southerly; it will then remain deflected towards the south for some 

2 Q 2 



300 LIEUT.-COLONEL S. G. BURKAKD ON THE 

hundreds of miles, and it will again become northerly as the Himalayas come into 
view. 

In spite, therefore, of the fact that the true direction of gravity at any one place 
cannot be determined with certainty, yet it is possible now to classify deflections of 
the plumb-line in India by regions. A modification of the spheroid of reference may 
alter values and may move the regional boundaries, but it will not affect the general 
correctness of the classification. A change in the assumed value of the direction of 
gravity at the station of origin will alter all deduced deflections of the plumb-line by 
the same amount, but it will not affect their differences, nor the mean differences 
between regions. 

I propose now to show : 

(1) The classification of stations by regions. 

(2) The effects on the classification of changes in the spheroid of reference. 

(3) The effects on the classification of the existence of a deflection at the origin. 

(4) The final values of deflections of gravity, corrected for errors of spheroid and 

origin. 

In Plate 1 5 India has been divided into four regions : 

(1) The Himalayas, (2) the zone of southerly deflections, (3) the Indian Peninsula, 
(4) North-west India. 

In the following four Tables III A., IIlB., IIIc., IIIo., which correspond to the four 
regions, the direction of gravity at Kalianpur has been assumed to be coincident 
with the normal to the spheroid, and has been adopted as the datum. The deflections 
of gravity are given in the columns headed (A G) ; the symbol A denotes the 
astronomical or observed value of latitude, G denotes the geodetic value of latitude, 
which has been calculated through the triangulation extended from the origin over 
the spheroid. 



INTENSITY AND DIRECTION OF THE FORCE OF GRAVITY IN INDIA. 301 



apnwpi 


a a 3 as/, s s 


Meridian of 88. 


i 


plojai(ds aiiJ^io 


5 3 !? 2 a " 

i i i i i i 


|i[(..i.ii|i[:J IK.I.I.I \;,| 


s g s s ss 

1 1 1 1 1 1 


jBpuno<i uwA*B[muiH 

UIOJJ 80UUJSIQ 


2 S S3 8 S "= SS 
6 1 1 1 1 + + 


4) - 

5 o 

* I 


g s "3 g -c g, 

i ? 1 s * t 

s ^ a s s 


Meridian of 86. 


i 

*4 


ploa9t(ds aitJ^lO 


a s 

1 1 


pIOJ9qd8 5S9J9A3 


5 S 1? 
1 1 


A"jupunoq UB^WJ-BUIIH 
uiojj aouwjsjo; 


J ?! S 
6 I i 


LJ 

11 


- *' 

5 5JS 

1 -1(2 
w s 


Meridian of 80. 


6 



pIOJ3qdS 8514B|3 


i 1C r-1 
T r-l 

III + 


pio-iaqds is9jOAg 


a - - 
1 1 1 


A~JBpunoq TiB^efBuiin 

UIOJJ OOUT^SIQ 


J S 8 S S 
a i + 


s 
B**$ 

ri 


its 1 

1 1 S 
a v, $, x 


Meridian of 7 30'. 


e 

i 


pjojaqds 9i(ji!o 


g 8 3 *> " ~ " 
II 1 1 1 + + 


pioaoiids is9.i9.\g 


^ O !~ ^) OJ lO O O 

ec w ^ 

II III 


ipimoq injAupmnji 
uioaj 90UB;si<j 


M s s s s s 3? g 

1 1 + 


o C 
8J 

ll 


63 

" ,.$.[* 

~ & O 3 

a - 1 j 1 1 t 

J ^^2^3 
t5 ca w 5 W w tn 


Meridian of 77 30'. 


1 

<1 


pioa3i[de gjjjuo 


W ' - <M *r> l - T -r> *-O C31 CC "> 'O iQ O r-t O 'O 
COOlCOtO-f^l IO 07 IM 1-1 

1 1 1 1 1 1 1 1 + 1 _l 


plOJ9l[ds 1S3J9A5I 


i -r TJ co i~ i - cv i- o i- > >o ' o 10 'O 
<S eo -* <S co w --i 

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 


foupunoq irB^eimuiii 

UIOJJ aoUtfJSifl; 


J 55-*'e *" i 
S 1 1 1 1 + 


CD G 

3*1 

* 0-5 

* 1 


llliilPPPiilils i 1 


Meridian of 75". 


t 


pioj9qds 9J(JB[0 


; rf> *f en IQ N 03 

1 1 + + + 1 


pToaaqds isajgAg 


s 8 *-* 

1 1 + + + 1 


Ajupunoq uwA'tti'BuiiH 

UIOJJ aOUBJSIQ 


J S S 8 8 S S 

i i + 


<D a 

. 


' ' J S ' 

1 1 1 1 1 1 

g t 5 1 g 1 s 

a_J_J__l_l 


9v>tH!}nq 


oS855 RS3S S 



302 



LIEUT. -COLONEL S. G. BUKKARD ON |THE 









epn, !m 


oSSSSS 3SS3 








O 


piojoqds oJ{aT!iO 


COOC1 fKr-trt^H 




s 


So 

00 


1 


p,o J oqd S , S a J OAa 


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H 


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w-wn 


ogSSKSS SSSS 





INTENSITY AND DIRECTION OF THE FORCE OF GRAVITY IN INDIA. 303 







apn W in 


"SSSSSS 83 2 - o n N-.OO. oo 










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7 


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H 


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t CO CO ^ O CO O iO t- C. 1^ --O 

ii i i T i 1111 


a 

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ii i + 1 7 1 1111 


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2 
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s 1 i 1 43 ' |lfl4 1 

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Q CM K 3 WSS > ^S PH 




d 


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III 1 1 1 1 i + "l '] 'l II 7T"| 1 + '+ + + 


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T 7 f T 7 '? T 7 + 7 1 T 7 T " 7 v T + + + + 


Meridian o 




o S 

s o 


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& 


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ra 1.0 o 

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oo 


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o c 

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3 ' 3 

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6 


piojoqd, o,. re , 


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p piojoi(ds ^soaOAg; 


M'? T77 T 'f'i i 'i ~+ +'+ T 'i + + + '+ 


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... ... . . . . . ....;_..,_ . . . . 


Meridian o 




s 
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to 


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p,,*, ,,, 


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i 


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7777+ t 7 T 'f + i+ M ii + 


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it- 2 

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fe 


i 


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304 



LIEUT.-COLONEL S. G. BUERAED ON THE 







,pn,,^ 


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1 

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t cqoooor-tio o 

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t 
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| 

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cfl 


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a 

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t- 


pio.icn[ds ^SO.IOAJI 


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3 

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r> -q 


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1 

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to 


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III 1 + 111 + 


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III 1 111 + 


1 
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Meridian < 


1 

to 

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ft 

= " "S , eft -3 
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atude of Kaliiinpur h 


i & 

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7 


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S 8 S R K S S S 





INTENSITY AND DIRECTION OF THE FORCE OF GRAVITY IN INDIA. 305 

TABLE H!E. 
Summary of the four preceding tables. 



Region. 


Number of 
stations. 


Mean deflection of the plumb-line. 


Everest spheroid. 


Clarke spheroid. 


{mountains . . 
plains .... 
Zone of southerly deflection . . . 
Indian peninsula 


19 
23 
43 

85 
27 


-35 1-15 

- 5 0-82 
+3 0-24 
- 3 0-28 
1 0-23 


-34 1-19 
- 4 0-83 
+3 0-24 
- 4 +0-28 
1 0-23 


North-west India 





It will be seen that in the Himalayas the deflections are northerly and large, but 
that as we move southwards from the mountains they decrease rapidly more rapidly 
in fact than the law of gravitation requires. 

As we recede still further from the Himalayas we enter the positive zone, and here 
we find a region 1000 miles long and 200 broad running parallel to the Himalayas, 
throughout which the plumb-line is always deflected towards the south. 

As we progress still further southwards we enter the Indian peninsula ; on crossing 
the boundary line between the 2nd and 3rd regions we find that the deflection of the 
plumb-line changes its direction and sign ; between latitudes 24 and 18, from coast 
to coast, strong northerly deflections averaging 6" now prevail ; as we move south- 
wards towards Cape Comorin these northerly deflections slowly decrease, and in the 
extreme south of India change to southerly. 

In North-western India the latitude observations have not brought to light any 
marked characteristic. This region is west of the Himalayas, and longitude deter- 
minations, if made at numerous stations, would be more likely than latitude 
observations to yield instructive results. 

The opinion had been expressed that the large deflections of 30" and 40", discovered 
in the sub-Himalayas near Mussooree and Phallut, might prove to be local and 
exceptional, and that it was unsafe to assume them characteristic of the region. To 
test the correctness of this view, Captain COWIE observed for latitude in April, 1903, 
at the Himalayan Station of Birond, and found that the direction of gravity was 
deflected here 44" towards the north ; in November, 1903, Captain H. WOOD, R.E., 
observed for latitude at two stations in Central Nepal and met with deflections of 
33" and 38". All the evidence that is slowly accumulating tends, therefore, to show 

VOL. ccv. A. 2 R 






306 LIEUT.-COLONEL S. G. BURRARD ON THE 

that these large deflections of gravity are not confined to exceptional localities, but 
prevail throughout a vast region. 

In October, 1903, Captain COWIE was directed to extend the Great Arc of India 
northwards across the Mussooree hills to the snowy range, and to observe for latitude 
in the inner Himalayas. High authorities had expressed the opinion that the large 
deflections of gravity at Dehra Diin, Birond, and Phallut were due not to the 
Himalayan mass, but to the peculiar geological formation of its lower and outer 
range ; that these deflections would be found to disappear when the first Himalayan 
ridges were crossed, and that large southerly deflections would be met with in the 
inner Himalayas. Captain COWIE extended the Great Arc of India into the 
mountains from latitude 30 29' to 31 1', a distance of 35 miles, and he observed for 
latitude at the Himalayan stations of Bahak (9715 feet high), Bajamara (9681 feet), 
Lambatach (10,474 feet), and Kidarkanta (12,509 feet). Table IIlA. shows that 
large northerly deflections were met with at all these stations. 

The form of the ideal section deduced in fig. 3, Plate 14, from pendulum results 
rather justified the belief that deflections would be found to decrease rapidly between 
Station 41 (Mussooree) and Station 43 (More). The northerly deflection of 30" now 
discovered by COWIE at Kidarkanta* consequently throws doubt on the correctness 
of that portion of the pendulum section that lies between these two stations, and 
confirms the opinion that a greater excess of matter exists at More" than has been 
deduced from BASEVI'S observations. 

In Plate 17 is given a cross-section of the Himalayas, drawn by Captain COWIE, 
through the stations of Kidarkanta and More" ; this section is not ideal but real ; it 
shows the variations in the actual level of the ground, and illustrates the visible 
mountain mass separating the two stations ; the vertical scale is twenty times as 
great as the horizontal. 

Plates 18. 19 and 20, drawn by Captain COWIE, give cross-sections of the Himalayas 
at Kidarkanta, Birond, and Phallut ; they illustrate the increase in elevation between 
the plains of India and the plateau of Tibet at three different places. In each the 
vertical scale is ten times as great as the horizontal ; the scales employed in these 
three last plates are larger than those used in Plate 17. 



* As an observer penetrates a mountain range, he leaves more and more of the mountainous mass 
behind him ; the attraction of the portion left behind is then opposed to the attraction of the masses still 
confronting him, and tends to decrease the resultant deflection of his plumb-line. To determine the 
relative effects of the rearward and forward masses a contoured map is necessary. 



INTENSITY AND DIRECTION OF THE FOECE OF GRAVITY IN INDIA. 307 

(5.) The Adoption of a New Spheroid. 

The deflections have so far been deduced from the Everest and Clarke spheroids 
only. It is now proposed to show the values that will be obtained if the Clarke- 
Bessel spheroid, as described above, be adopted. 

In the Tables IVA., IVu., IVc., IVD., and IVE. is given the inclination at every 
station between the observed level surface and the surface of the Clarke-Bessel 
spheroid. 

The inclinations are stated, firstly, when that at Kalianpur is taken as zero, and, 
secondly, when it is taken as +6". The reason for adopting this latter assumption 
will be explained in section (G) on the zero of verticality. 



2 B 2 



308 



LIEUT.-COLONEL S. G. BURRARD ON THE 



apnwuq 


x 8 a s s s s s 


N.B. In the column headed " Distance from Himalayan Iwundary," the negative sign opposite a station denotes that the station Is situated within the Himalayas. 


dian of 88. 


*|ll 

m{ 


,,9+ sn andu^nnH 
0} pMjapji 


8 8 8 S 2 - 
i i i i i + 


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0? P3JJ8J3JI 


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1 1 1 1 1 1 


repunoq UH^IBUIIH 

uiojj ooainsKI 


| S 8 S " 8 
a i i i i + + 


S 


c 

H 


* ' 1 

g 3 - D 
1 f 1 IIS 

d< H M 5 ^ 


Meridian of 86. 


till 

ii*| 


()+. SI! 41ldtIBIlJI 
0} P9JU9PH 


S S 
1 1 


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0} pjj9ja;[ 


? a s 

l l 


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UIOJJ OOllW^SIQ 


J S8 S 

'i i i 


o C 

S- 

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!5 -2 


Sg 

= II 

3 i 
w a 


Meridian of 80. 


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<)+ si; .uniuvn 1! H 
0} p.u.iojaji 


i -n w c* t- 

cc 

11+ + 


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II 1 1 1 + + 


XjBpunoq inj.ftqimijH 
uiojj aouitjsif]; 


1 83 83$23 
i i + 


cu 

s 


<D C 

SM 

1 


II 1 ill! 

MA w 35 CQ GO 3 


Meridian of 77 30'. 


<?ill 

J,S2 
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01 


',,9+ su .uidu^qii}! 

0^ p3JJ3JS)i 


lOCTi^rCOiO Qi 00 < tO M M CQ l- 00 W W 

w;i^c^i':w fi oi 

Illlll 1 1 II+ + + + + + + 


OJ9Z eit jnduijiIU3 

01P9JJ3J9H 


5 r (lOOf'CtO'C'r QO i I tf5 *# ^ t 1 i 1 ^" 1/3 

MCTcort-JS ro S 

Illlll 1 1 1 1 1 1 1 + + 1 1 


jtnjpunoq irejCv|HiuiH 

UIOJJ 90U^J<H(I 


| <joo^^o<o<o '"SSSSSg | g 
1 1 1 1 + 


1.1 
* 1 


1 - : i : : | : | '. |i* : . . : . 
1 ! 1 1 J 1 1! l! iK i i 1 1 1 *' 4 l 

^wiSaa^nQQ wso!5 < & 


Meridian of 75. 


j r^ 
^jj? P 

I|I| 


,,9+ ire jnduTJn3 * 3 "* 2 S S * 
o^pauajaH | , + + + + + 


OJ9Z sv jndu^ii^jj 

0} P8JJ9J3H 


i 5D CT 'S* t- -<Jl ^H 
1 1 + + + 1 


^jpunoq UB.?B]BUIIJI 
uioaj aoutfjsiQ 


J 8 S S 8 S 

l_j+ " 


v C 

i'S'l 
* 1 


ililli 

S i 1 1 1 1 


epnwvi 


3 3 S 8 S S S S 



INTENSITY AND DIRECTION OF THE FOECE OF GRAVITY IN INDIA. 309 





pnwi 


^8s ssj a ssas 


a* 


<j> jiH i-d '" 9 + JndlI V!lX 01 IKUJ3J3}[ 


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38 
S 


"'QCS "> * 'O43Z SB jnduyi|BJ[ O1 P3.U3J3JY 


^ eo 10 ^i ^<OO.H 
+ + + + I 


Meridian 


H 


1 ! ! 1 1 3 a 

111 ill! 

3 g g lisa 




f Ills : '" 9+ 8 " jndu? B i > P 3 -" 9 ^ 


* Oi 


05 

"o 


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a n 


Meridian 


B' 

|.,| 

la ^ 


\ 




- 


&~% i_- '//9+ BB jndnyi|Bjj <xj pojjnj3j^ 


* ? 


00 

*o 


Q ^ M ^ 'O.I3Z SB Jlldliy t \vyi O^ p3JJ3J3JJ 


^ O 


Meridian 


^l 


be 

| 

3 

K 


R . 


tSU A '//{)+ s Jtidtninuw o 1 ) pn.uoiojr 
" SjS 


S -i> Cl 


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^ O C 1 ? 


Meridian 


o a 
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i ! 

w 5 


. 


f il ss '" 9+ rajn(Ini "i 1! M i P 9 - 1 ^'! 


C4 ~ C4 <N O OD lO t- O O 


*o 


*! o S) " * 'OJ3Z SB JlldnVUBJI OJ p3.U3JO}[ 


+ + + + + i + T + 


Meridian 


1^1 
* 1 


g .... 

1 1 1 1 1 tli! 


8 


S^l i^j '//+ SB jndtiv!lB3 01 \JJ3J3}[ 


__ 01 o 01 i- -n 


fe 


<! 5 ! S" . OJ3Z 8 B andHBHBX O, P3J..3J3,, 


? + + + + 


Meridian o 


M 


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g -5 : = * 2 o 
5 V *> g S 'H ^ 

O S ^ < Q O o5 


1 


i. i 1 i ^ ',,9+ .nduviIBX 05 iwjasjajr 


t 2 


S 


3^ 6 ag 


O " -" M 1-1 1 .-( i-t 

+ + + + + 1 + 


Meridian o 


I 
"1 


ms^Ti ; ; 

II? ^^ i & = * 
g 1 1 i gsl i = 1 i 

^^.t = a.g^ S.S 

M PMHtnm MM>-)EH 




f "8 B^S _!- ' 


CO . 


? 


***Qra * * 'oaaz SB jndu^tj^ 01 pajjajajj 


? + 7 


Meridian 


H 

^ 


J - 

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"m 3 

M 1-3 O 




jt 1 i TJ "9 + SB jndnBHBX 0} psaaajsa 


= +55+ * 





*t Q W u 'OJ3Z SB anduBIVBX OJ p3JJ3J3JI 


+ ? + + ? 


1 


H 


ill! i 




Bpn,,,^ 


ogSSS S8 S 883 



310 



LIEUT.-COLONEL S. G. BUERAED ON THE 



_c 
EH 



3 

M 



9 pn,, m 


= 8 8 S S3 S S3 83 2 S 2 S S 3 332* 


Meridian of 86 and 88. 


li 


'" 9 t"^pa* 2 


+ + ii 


ojoz eu jnduijiiuH 


^ 10 ra I-H oo 
II II 


|*| 


. . ^o 

1 ^ 1 

a v 1 1 

3 S J 


Meridian of 82 and 84. 


Ulii 


'" 9 Vp3PK FH 


CM Ol O" ^ O I -l CO <D * CO 
+ + + + M 1 1 1 1 


QJOZ su andujji[TJX 


TJ< * co <N CD re L- ^ 2 2 ^ 

ii i i i7 1 i i i i 


Il 


... g g 
' s ' I '.'.". 1" = - ' 1 

' x EB <P H - 3 rt d 
ce ^ "3 -2 * 13 pel . 3 * S 

| | | | 111 |**|| 1 


Meridian of 80. 


j,|i-|| 


',,9+ SB jnilujiiiBH 


> KM co ON-* o-* --** -j-ra tj- w 


O.IDZ su jndupi[nx 


SO Cl 33 Ol X i ( "-C ^1 iC ~ d " l- -f X l t Tt< O i^ O 

i i i i ii7ii i77 7i MIII + 


o a 
g-.2 

s o-e 


"" 1 


v ^ J '5 ' -i 'a ^ v > c o so, S B 1 c ._' ^ ^ S 
ft |-| 1 ='= Sa -S^c? 1 S g"3-g 19 2 g g 
I'f | ;||-g Si H-S S S SfiJS -= ' S s 1 


Meridian of 78 30'. 


tils! 


,,9+ su .iinlin:i|^jl - ^ ~ co 
o^ p;).i.i,)].);[ + 1 


04 po.uopjj 


T 7_J 


o d 

e^.| 


1 SB 

3 g 

1 1 1 


Meridian of 77 30'. 


j,l|tl 


,Q+ si: .inilinMiir-vr - ^ - ^ oiccco 01 o <-* r- co r- ^ iox ^ 4 co NNdrK 
OJpOJJOJOH " + + + III 1 + 1 ++++1*1 + + + + 


'OJOZ S^! JlldulMimj - ^ -o to aj OV OV 00 too 1- G~* 10 rH rH N CO Oi 10 1* IO O 

01 po.u.iirm ' III III III 1 1 1 1 1 + 1 1 1 1 1 1 


s'S'-a 

feq | 


Ji in : it } i Mi 

^- -H S "^ = S 'o *5 1 , p "S ^ >c i " S 5 3 3 3 


Meridian of 76. 


r ^ 


'" 9 t^o!u d ,0)I l ' !H 


i >C i ' O 

1 1 


<|3& 


OJOZ 613 .UHllIJIIITJ^I 

o^pojjojoji 


^ Ol l^ to 

7 i i 


o c 
St. .2 

i 


535 
3~ * 


Meridian of 74 and 75. 


i|te 


"" 9 ^aSi ra 


-f 7 7 + + 7 o ".^ | + -| + 


'oaoz SB andujsiiujf 


i i i i i i 7 i i M i i i i i 


a e 


... . . . >. . s .... 
',.. . S . g = g 

I ! 1 5 i I til il if II i 

^rtgot-^ ^cd'CCte -.^^ >HCfc. C 

3 < G a H > n wsS gs KM KM s 


Meridian of 73. 


fljll 


'"^"p^aOT 1 * 3 


11+ 7 


OJ9Z SB induijipsx 


5 00 03 U5 CO 

1 7 i 7 


(G 


ii i ^ 

nS 1 6 


apnanirr 


g?iD-*co<MrH pa> oo t- io^< coM^oaioo 






INTENSITY AND DIEECTION OF THE FOECE OF GRAVITY IN INDIA. 311 







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312 



LIEUT.-COLONEL S. G. BUERARD ON THE 



TABLE 
Summary of the four preceding tables. 



Region. 


Number of 
stations. 


Mean deflection of the plumb-line Clarke-Bessel 
spheroid. 


Referred to Kalianpur 
as zero. 


Referred to Kalianpur 
as +6". 


(" mountains . 
Sub-Himalayan < 
L plains . . . . 

Zone of southerly deflection . . . 
Indian Peninsula 


19 
23 
43 

85 
27 


// // 
-33 1-24 

- 3 0-87 
+3 0-26 
- 6 0-23 
0-25 


// // 

-27 1-25 
+3 0-87 
+9 0-26 
0-24 
+6 0-24 


North-west India 





We can now judge of the effects of the substitution of the Clarke-Bessel spheroid 
for EVEREST'S by comparing the values given in the columns of Tables IVA., IVB., IVc., 
IVc., headed "Eeferred to Kalidnpur as zero," with the values given in Tables IIlA., 
IIlB., IIIc., HID. It will be seen that the large Himalayan deflections are slightly 
decreased, and that the positive tendency of the second region has been accentuated. 

There is a marked difference between the values of Table IIIc. and the values 
"Referred to Kalianpur as zero" in Table IVc. The progressive decrease in the 
observed deflections, from latitude 24 to latitude 8, as exhibited on the spheroids of 
EVEREST and of CLARKE, had led me to believe that the direction of gravity 
throughout Peninsular India was being influenced by some external excess or 
deficiency of mass, such as the Himalayas or the Indian Ocean.* The southerly 
deflections, shown in Table IIIc., at the extreme south of India, were attributed by 
General WALKER to the condensation of submarine strata, t The introduction of the 
Clarke-Bessel spheroid eliminates at once both the progressive decrease and the 
supposed southerly deflections in South India, and substitutes for them throughout 
the peninsula a large apparent northerly deflection averaging G". The introduction 
of the Clarke-Bessel spheroid shows that the progressive change exhibited by 
Table IIIc. in the inclination of the level to the spheroidal surface from latitude 24 
to latitude 8 was due, not, as I had supposed, to the deformation of the level surface, 
but to the abnormal curvature of the surface of EVEREST'S spheroid. 

* Professional Paper No. 5 of 1901, "Survey of India;" Monthly Notices, 'Royal Astronomical 
Society,' January, 1902. 

t 'Phil. Trans. Roy. Soc.,' vol. 186, 1895. 



INTENSITY AND DIRECTION OF THE FORCE OF GRAVITY IN INDIA. 313 

(6.) TJie Zero of Vertically. 

Tables IVA., IVs., IVc., IVo., and IVE. show in terms of the old datum, namely, 
with Kalianpur as zero, the angles of inclination in the meridian that have been 
determined in different parts of India between the level surface and the surface of the 
Clarke- Bessel spheroid. The difference between any two of these angles of inclination 
is affected only by changes of spheroid, but the absolute value of every angle is based 
on the assumption that the level and spheroidal surfaces are parallel at Kalianpur. 
Any alteration in the assumed inclination of the two surfaces at this our initial station 
will affect the inclinations as deduced at other stations by a constant quantity. The 
direction of gravity at Kalianpur has been adopted by the Survey of India as the 
datum, from which deflections of the plumb-line at all stations are measured ; the 
direction of gravity is, we know, always perpendicular to the level surface ; at 
Kalianpur it has been assumed to be perpendicular to the spheroidal surface also. I 
propose now to deduce a new value for the deflection of the plumb-line at Kalianpur, 
and to exhibit the values of the deflections of the plumb-line in India that will be 
obtained, if the deduced direction of gravity at Kalianpur be substituted for the 
original one in other words if our zero or datum be corrected. 

The direction of gravity throughout the first, second, and fourth regions appears to 
be under the influence of abnormal attractions ; there is, I believe, no other area in 
the world in which the deflection of the plumb-line undergoes at once such large and 
such systematic variations as it does in the two first regions of Plate 15 ; these 
observed peculiarities, too, have been discovered to exist in the neighbourhood of 
extraordinary mountain masses, and though the connection between the observed 
phenomena and the visible protuberances is obscure, there can be little doubt that the 
latter are in some indirect way the cause of the former. 

The direction of gravity in the fourth region also is probably influenced by the high 
mountains of Central Asia, though their effects are not directly perceptible. We 
will, therefore, omit from present consideration the results obtained in the first, 
second, and fourth regions, and we will confine our attention to those of the third 
region only. 

The third region is in the form of a trigon with its apex at Cape Comorin ; its 
length from north to south is 1100 miles, and its greatest breadth 1300 miles; its 
area is 750,000 sq. miles. This trigon is one of the oldest portions of land surface 
now existing on the earth ; it is mostly composed of ancient gneiss, and though a 
large part was covered in the cretaceous period by volcanic overflows, it suffers now 
but slightly from earthquakes and is exceptionally stable. This trigon appears to be 
as free from abnormal sources of disturbance and to be as suitable for the determination 
of the absolute direction of gravity as any area of land can be. If we examine the 
results "Eeferred to Kalianpur as zero" in Table IVc., we find that out of 
85 determinations of the direction of gravity made within the third region, 80 show a 

VOL. CCY. A. 2 S 



314 



LIETTT.-COLONEL S. G. BURRARD ON THE 



northerly deflection, two show a southerly deflection, and three show the direction of 
gravity to be vertical. The mean deflection throughout the trigon is 6"'4 North. 

Now if we are to accept these results as final, we shall have to believe that 
throughout the third region the level surface is always inclined by 6"'4 to the 
spheroidal surface. We know of no cause tending to produce such an extraordinary 
deformation, and we are led to suspect the reasoning by which its existence has been 
inferred. The only certain fact that has been brought to light by observation is that 
the plumb-lines in the trigon have a northerly deflection greater by 6"'4 than the 
plumb-line at Kalidnpur. We have, however, taken a step in advance of this safe 
ground, and have assumed that the direction of gravity at Kalidnpur is vertical, and 
that consequently the plumb-line throughout peninsular India is deflected 6"'4 towards 
the north. Would it not be more reasonable to assume that the mean direction of 
gravity throughout the third region is vertical, and that the plumb-line at Kalidnpur 
is deflected G"'4 towards the south ? The assumption of a southerly deflection of 
G"'4 at Kalianpur will lead then to the conclusion that throughout the third region 
the level surface remains generally parallel to the spheroidal surface. 

From visible evidence Kalidnpur, situated as it is in flat plains, would be adjudged 
a suitable datum station, but it unfortunately lies in the zone of southerly deflection, 
and its plumb-line is thus exposed to the horizontal attractions of hidden masses. 

If our geodetic operations had been confined to the third region, and if our datum 
station had been originally selected within this region, we should not have been led 
to suppose that its whole area of 750,000 sq. miles was abnormally affected. If we 
had subsequently extended our operations to Kalidnpur, we should have discovered 
there a southerly deflection of about 6", and this we should have adopted without 
question. 

TABLE showing the Number of Observed Deflections in the Third Region 



If we assume that the meridional deflection at 


Lying between 


Kalianpur is 




. 


+ G" (south). 








-12-5 and -14-5 


2 





-10-5 -12-5 


7 





- 8-5 -10-5 


13 





- 6-5 - 8-5 


18 


2 


- 4-5 - 6-5 


23 


5 


- 2-5 - 4-5 


10 


15 


- 2-5 


8 


22 


+2-5 and 


4 


24 


+ 4-5 + 2-5 





9 


+ 6-5 + 4-5 





6 


+ 8-5 + 6-5 





2 


Total .... 


85 


85 



INTENSITY AND DIRECTION OF THE FORCE OF GRAVITY IN INDIA. 315 

The southerly deflection at Kalianpur of G"'4. which has been deduced from 
plumb-line observations, is to a certain extent corroborated by the section drawn in 
Plate 14, fig. 3, from pendulum observations ; if we assume that the errors in BASEVI'S 
pendulum results will be found constant, the section will be raised with reference to 
the sea-level, but will not be otherwise affected ; and if we regard the distribution of 
mass exhibited by this section, and calculate the deflection at Kalidnpur by means of 
CLARKE'S formula (' Geodesy,' p. 298), 

f /' l\<i&nW /,,\ciu2<7 /7/\2A-| 

A = P log. {(I) . (y . (~) \+2p{c'<j>' sin 2 c/-c4, sin' cr}, 

we obtain a value of +5"'!.* 

In Tables IVA., IVu., IVc., IVD., IVE., in the columns headed " Referred to 
Kalidnpur as 4-6"," the values of deflections have been exhibited on the assumption 
always that the plumb-line at Kalidnpur is deflected G" towards the south. 

(7.) Summary. 

A comparison of the two values given to each deflection in Tables IVA., IVs., IVc., 
IVD., and IVE. will illustrate the effects of the adoption of the corrected datum ; the 
large Himalayan deflections, it will be seen, have been slightly decreased ; they amount 
now to about half the theoretical values derived from an application of the law of 
gravitation to the visible mountain masses ; the sudden diminution of the large 
deflections at the foot of the mountains is still very remarkable. 

The great zone of southerly deflection has been expanded both to the north and to 
the south, and it now includes many of the stations classified in the first and third 
regions; for instance, in the sub-Himalayan region (Table IVA.), the stations of 
Kaliana, Bansgopal, Jarura, and Jalpaiguri exhibit southerly deflections when the 
corrected datum is used; in the Indian Peninsula (Table IVc.) the positive zone has 
been extended southwards to Thikri, Ladi, Hathbena, and Chandipur ; in North-west 
India (Table IVo.) every station now presents a marked southerly deflection; and the 
positive character of the deflections in the positive zone itself (Table IVs.) has been 
strongly accentuated. 

To the north of the second and fourth regions stand the mountain masses of 
Central Asia, but throughout those regions the direction of gravity is systematically 
deflected towards the south. That the direction of gravity should be deflected 
everywhere towards the south with a mean inclination of 8" throughout an area of 
half a million square miles (Tables IVB. and IVo.) is an extraordinary phenomenon 
of nature, and this phenomenon has been observed on flat low-lying plains bounded 

* Attraction at Station 24 of mass lying north of Station 38= 1" - 61 
24 south 38 = 6" -67 

5" -06 

2 S 



316 LIEUT.-COLONEL S. G. BURKAKI) ON THE 

on the north by mighty mountain ranges and tablelands. Deficiencies of density 
underlying and compensating the highlands, on whatever assumptions of depth they 
may be based, will be found insufficient to account either for the prevalence or 
mao-nitude of these southerly deflections; that the mountains and deflections are, 
however, in some way connected can hardly be doubted. The section in fig. 3 
of Plate 14 perhaps justifies the inference that the general deflection of gravity 
towards the south is being caused by deficiencies, underlying not the mountains 
themselves, but the plains in the immediate vicinity of the mountains. 

All our pendulum and plumb-line stations situated actually in the Himalayas have 
so far been located on peaks ; the results deduced have therefore been obtained from 
the highest points in the several Himalayan districts visited. It is important that 
observations should be taken at stations situated in the deep valleys of the inner 
Himalayas. The difficulty of fixing such stations by triangulation has hitherto 
limited observations to summits, but it is necessary now that we should ascertain 
whether the subterranean deficiencies underlying the Himalayas vary in amount with 
the heights of the superincumbent mountains, or whether in their compensation of 
the mass as a whole they remain independent of the altitudes of the alternating 
ranges and valleys above (see fig. 2, Plate 14). 

Another question of interest has arisen, namely, whether the southerly deflections of 
the second region merge gradually along the border line into the vertically of the 
third region, or whether there does not exist an intermediate longitudinal area in 
which northerly deflections prevail. A study of Table IVc. will show, I think, that 
throughout a strip immediately south of the dividing line the deflections have a 
tendency to be uniformly northerly.* The cross-section in fig. 3 of Plate 14 shows an 
excess of mass to underlie Kalianpur (Station No. 24), and this excess is possibly a 
contributory cause both of the southerly deflections of the second region and the 
northerly deflections in the parallel strip. The continuance of similar deflections both 
to the east and to the west of Kalianpur lead me to think that the pendulum 
observations of the future will furnish on all Himalayan meridians cross-sections 
similar to that given in the figure. 

Geodetical observations have shown that the density of the earth's crust is 
variable, but they have not given any positive indication of the depths to which these 
observed variations extend. All calculations of the effects of subterranean variations 
in density and of mountain-compensation have, therefore, to be based on arbitrary 
assumptions of depth. The fact that the plumb-line seems generally to respond 
readily to results given by the pendulum, perhaps justifies the inference that the 
observed variations in the density of the earth's crust are not deep-seated. If an 
abnormal amount of matter exists in the crust near the surface, it will exercise direct 
effects upon plumb-lines and pendulums in the vicinity, but if it lies at a great depth, 
its effects, especially on plumb-lines, will be less perceptible. 

*Vide stations Chaniana, Valvadi, Badgaon, Aiikora and Mai. 



INTENSITY AND DIRECTION OF THE FORCE OF GRAVITY IN INDIA. 317 

We have not at present sufficient pendulum stations to warrant definite conclusions, 
but we can make use of those we have to test whether the observations of the 
intensity and direction of gravity tend to corroborate one another.* The cross-section 
in fig. 3 of Plate 14 gives the result of pendulum observations at stations on the 
meridian of 70 30' ; the direction of gravity at these and intermediate stations is 
shown referred to Kalitlnpur as +6" in Table IV A. for all places north of latitude 27, 
in Table IVfi. for places near latitude 25, and in Table IVc. for all places south of 
latitude 24. We can therefore institute the following comparisons : 

(1) The pendulum section would lead us to expect a large northerly deflection at 

Station 38, and Table IVA. shows that at this station (Dehra Dim) the 
deflection is 29" north, f 

(2) From Station 38 to Station 24 the pendulum indicates a gradual increase in the 

density of the crust ; the plumb-lines confirm this increase in a remarkable 
manner. 

(3) At Station 24 (Kalianpur) the pendulum indicates the existence of a greater 

amount of subjacent matter than underlies the stations on either side of it. 
Tables I. and II. show this more clearly than the section. Now, if we look in 
Table IVi3., we find that from Kesri to Tinsia the plumb-lines are all deflected 
south towards Kaliiinpur, whilst if we look in Table IVc. we see that from 
Takalkhera to Badgaon the plumb-lines are deflected north towards Kalianpur. 
Thus the existence of an excess of matter in the crust indicated by the 
pendulum at Kalianpur is confirmed by the action of the plumb-lines on both 
sides of it. 

(4) The pendulum section shows a considerable excess of matter to underlie 

Stations G and 7 (Bangalore). Now, if we look at Table IVc., we see that the 
direction of gravity is much disturbed in the neighbourhood of Bangalore. 
At the two base-line stations near Bangalore, the deflections are northerly ; 
sixty miles north at Bommasandra the deflection is 8" southerly. The 
inference is that an intermediate excess of matter exists, and that a station 
could be found north of Bangalore at which the pendulum would indicate a 
greater excess than at Bangalore itself. (The section had to be drawn 
from station to station, but if intermediate observations were to be taken, 
it is certain that the maxima and minima of the section would be slightly 
moved.) 

(5) Table I. shows that the force of gravity was below normal at all BASEVI'S 

inland stations but Calcutta ; for this reason Calcutta has hitherto been 

* It is true that the results of the old pendulum observations are not correct, but their errors are mainly 
systematic and though affecting absolute values do not vitiate differences. Differences are sufficiently 
accurate to justify the comparisons instituted. 

t The names of the numbered stations of the section are given in Table II. 



318 THE INTENSITY AND DIKECTION OF THE FORCE OF GKAVITY IN INDIA. 

classified as a coast station. It is, however, 100 miles from the coast and is 
in truth less of a coast station than Kew or Greenwich. It was probably 
included amongst coast stations because BASEVI obtained there a positive 
result which accorded with his results at Madras and Bombay. But his 
positive result will, I think, be found in the future to be due not to 
Calcutta's proximity to the coast, but to her situation over the long chain of 
excessive density that is believed to run parallel to the Himalayas from 
west to east, and that is indicated in fig. 3 of Plate 14 by the position of 
Station 24.* If we examine the last columns of Tables IVB. and IVc., we 
see that the deflections are south at Calcutta and Dariapur, but north at 
Cuttack and Khundabolo. 

(G) If an observer working over the plains of Northern India were to trust only 
to his eye and his level, lie would record the existence of a great mountain 
range to the north and of low hills or flat plains to the south ; if, however, 
he were to disregard the evidence of the eye and of level, and were to believe 
either his pendulum or plumb-line, he would come to the conclusion that he 
was standing between two mountain ranges, one of which, visible to the north, 
was rising abruptly out of the plains, whilst the other, invisible to the south, 
was slowly gaining in elevation for 300 miles. 

I have taken several instances of abnormal pendulum results from Table I. and 
have found in each case a direct response from the plumb-lines at neighbouring 
stations. This conformity could hardly ensue if the variations in density extended to 
greater depths than 30 or 40 miles. Our results do not justify us in asserting that 
HO deep-seated variations in density exist, but they do justify the belief that the 
variations in density which have been discovered are apparently superficial. 



* When I write of the excessive density of the earth's trust, I am judging from local observations only. 
I mean, therefore, " excessive " compared with surrounding portions of the crust, and not with the mean 

surface density of the earth. 



[ 319 ] 



IX. On the Refractive Index of Gaseous Fluorine. 

By C. CUTHBERTSON and E. B. R. PRIDEAUX, M.A.. JB.Sc. 

Communicated by Sir WILLIAM RAMSAY, K.C.B., F.K.S. 

Received June 5, Read June 8, 1905. 



THOUGH fluorine was isolated by M. MOISSAN as long ago as 1886, no attempt has 
hitherto been recorded, so far as we are aware, to measure its refractive index in the 
gaseous state. This omission is the more to be regretted since great interest attaches 
to the determination. Not only is fluorine the first member of an important group of 
elements, but its power to retard light, calculated from the refract ivities of its 
compounds, appears to vary within unusually wide limits, so that the estimates of its 
refraction equivalent are singularly discordant, and agree only in shmving that it 
must be remarkably low. 

Thus, Dr. J. H. GLADSTONE* originally gave the refraction equivalents of fluorine 
and chlorine as 1'4 and 9 "9 respectively, figures which correspond to a refractive 
index for fluorine of TOOOIOS, or considerably less than that of hydrogen (1 '(100139). 
In 1885 1 he placed it at I'G. In 1886 G. GLADSTONE^ put down the refraction 
equivalent at between 0'3 and 0'8, and in 1891 the same observer, with Dr. J. H. 
GLADSTONE, estimated it as "extremely small, in fact, less than TO.'' More recently 
MOISSAN and DE\VAR,|| judging from the appearance of liquid fluorine, recorded their 
belief that the index would be found to be higher than had previously been supposed, 
though still low in relation to its atomic weight. 

In these circumstances it seemed desirable to attempt to measure the index of the 
element in the gaseous state, and with this object Mr. CUTHBERTSON visited Paris in 
January, 1904, and, by the kindness of M. MOISSAN, was enabled to observe the index 
of a current of fluorine passing through a small hollow prism of copper, the apertures 
of which were covered by plates of fluor spar. A summary of this work has already 

* 'Phil. Trans.,' vol. 160, p. 26, 1870. 
t 'American Journal of Science ' [3], XXIX., p. 57, 188-j. 
J 'Phil. Mag.' [5], XX., p. 483, 1885. 

J. H. GLADSTONE and G. GLADSTONE. 'Phil. Mag.' [5], XXXI., p. 9, 1891. 
|| MOISSAN and DEWAR, 'Proc. Chem. Soc.,' XXXI., p. 175, 1897. 
VOL. CCV. A 395. 19.10.05 



320 iMESSRS. C. CUTHBERTSON AND E. B. K. PRIDEAUX 

been published,* but the following details are added in order that the value of the 
experiment may be criticised. 

Table I. exhibits the results obtained in five experiments, performed on two 

occasions. 

TABLE I. 



Number. 


Date. 


Refractivity 
01-1)10". 


Time of flow of gas. 


1 


January 13, 190-4 


232 


25 minutes. 


') 


13, 


228 and 226 Not recorded. About half-aii-hour additional. 


3 


20, 243 


About half-an-hour. 


4 


20, 2-41 


An additional quarter of an hour. 


5 


20, 


227 


An additional half-hour, with another electrolytic tube. 



These figures require some explanation and comment. The refractivity of fluorine 
is certainly much lower than those of oxygen and nitrogen, while that of all other 
elements (except hydrogen, helium, and neon, the presence of which need not be 
suspected) and, tt fortiori, of all compounds,! is higher. Consequently, when air is 
displaced from a prism by fluorine, the lower the index observed the nearer do we 
approach to that of the latter. 

The first experiment recorded in Table I. may be discarded. During its progress 
an unaccountable change of zeros took place, which makes it doubtful whether the 
reading given above, or a lower one ('215), should be accepted. The balance of 
probability is in favour of the higher value. 

When the prism had been swept out with dry air the second experiment was 
performed, and gave two trustworthy readings of 228 and 22G for the refractivity of 
the contents of the prism. 

After making some improvements in the stability of the apparatus and substituting 
tubes of finer bore (about '2 millims.) for the old leads, a second attempt was made on 
the 20th January. 

On this occasion a very trustworthy experiment gave a refractivity of 243, or 16 
points worse than that of the second experiment of the 13th January; while a second 
trial, made after recovering the zero by sweeping out the prism with air, gave an 
almost identical result, 241. 

It was then suspected that the electrolytic tube had developed a leak, and a new 
one was substituted. 

The fifth experiment, performed with this apparatus, at once gave a refractivity of 
227, which is nearly identical with the best experiment of the 13th January. 

* 'Phil. Trans.,' A, vol. 204, 1905, p. 323. 

t A molecule of HF probably retards light less than a molecule of fluorine, but since the molecule of 
this vapour, under normal conditions, is at least as complex as HoF-j, its presence in an atmosphere of 
fluorine would probably raise the refractivity of the mixture. 



ON THE REFRACTIVE INDEX OF GASEOUS FLUORINE. 



321 



In all these trials a singular fact was observed. The index slowly decreased to a 
minimum, and, after remaining steady for a few minutes, retrograded by several 
points, indicating the presence of an increased proportion of some gas of higher 
refractivity. This effect was observed in nearly every subsequent experiment 
performed with the prism, and its significance will be referred to hereafter. 

But, in spite of the concordance between the lowest values obtained on the first 
and second days, these experiments could not, for several reasons, be regarded as 
satisfactory. All previous estimates of the refractivity of fluorine, based on the 
refraction equivalent, point to a much lower value than 227 ; and, though this 
expression cannot be relied upon to give a very close approximation, its agreement 
with the refractivity is usually fair, and there is no other instance of so wide a 
discrepancy between the two as these figures would show. 

In the second place, it was not certain that the current of gas employed, which 
was at the rate of l to 2 litres per hour, would completely displace, from the train 
of purifiers, a volume of 100 cub. centims. of air, whose density is not far removed 
from its own. And, thirdly, the retrograde motion of the index after reaching a 
minimum, and subsequent slight variations, definitely proved that the contents of the 
prism were not homogeneous. 

For these reasons the authors determined to undertake a further investigation of 
the subject, using the apparatus with which Mr. PRIDEAUX had, by this date, 
succeeded in obtaining fluorine, by the method of M. MOISSAN. The form of the 
electrolytic tube employed may be seen in fig. 1. It was kept cool by means of a 





Fig. 1. 

mixture of alcohol and solid carbonic acid, in such proportions as to form a paste. 
The current ranged from one to two amperes. In two or three minutes the voltage 
usually ran up to its steady value, and, soon after this, a piece of blotting paper, 
wetted with alcohol, when held near the exit tube gave abundant fumes of HF 
and then burst into flame. When this was observed the U-tube was connected to 
the train of purifiers and prism or refractometer tube by means of a well-fitting 
platinum junction. 

Many experiments were made with this apparatus, but the results were not more 

VOL. ccv. A. 2 T 



322 MESSRS. C. CUTHBERTSON AND E. B. R. PRIDE AUX 

concordant than those obtained in Paris, and suggested, as in that case, that the 
current of fluorine was not sufficiently rapid to displace completely the air in the 
coolers and tubes. 

It was, therefore, decided to liquefy the gas as it was produced, and, when sufficient 
had been collected, to allow it to boil off rapidly through the prism. This was done 
with the arrangement shown in fig. 1, but the results showed no improvement, and it 
seemed probable that some oxygen, either from the air or some other source, was 
condensing with the fluorine, the boiling-points of the two elements being very nearly 
identical. 

These experiments led to the conviction that it was practically impossible to obtain 
fluorine in a state of absolute purity.* And since no means could be devised for 
removing the gases by which it was accompanied without affecting the fluorine, it 
was decided to have recourse to an analysis of the mixture of gases whose refractivity 
was observed, and to correct for the impurities detected. For this purpose the prism 
method was found unsuitable and JAMIN'S refractometer was substituted for it. 

The plan at first adopted was to displace the air in the refractometer tube by a 
current of fluorine, counting the interference bands as they passed across the field, 
owing to the change of refractivity. When a steady state was reached the tube was 
disconnected from the source of fluorine and its contents collected over dry mercury, 
by filling it with mercury from a reservoir. t It was anticipated that the fluorine, on 
being bubbled through mercury, would instantly be absorbed as fluoride, and that 
the residual gases could be measured and analysed. In a second set of experiments 
glass tubes were used, and the residuals were collected over a standard solution of 
soda. Here the reaction expected was the absorption of fluorine and production of 
half its volume of oxygen, according to the equation 

2F 2 + 4NaOH = 4NaF + 2H 2 + O 2 . 

The principal figures connected with these experiments are given in the following 
table : 



* Even in his most recent density experiment M. MOISSAN, after a prolonged trial with a current of 
5 amperes, found 5 4 78 cub. centims. of nitrogen still left in a density bulb of volume 159-2 cub. centims., 
or 3| per cent, of impurity. ' C. R.,' 138, p. 731, 1904. 

t A new refractometer tube was made for each experiment, when copper tubes were used. 



ON THE REFRACTIVE INDEX OF GASEOUS FLUORINE. 



323 



oo 
T3 

rH 

I 



> 
<B 



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03 
03 
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09 



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53 

PH 

X 

W 



W tJ 

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* 

to 
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=e ^ 

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6 o 3 5 3 5 ooo 


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2 T 2 



324 MESSES. C. CUTHBEKTSON AND E. B. R. PEIDEAUX 

These results are not concordant, and the causes of the discrepancies were not 
completely disentangled. It will be sufficient, therefore, to indicate, briefly, their 
probable nature, without attempting detailed criticism which the figures will not 
bear. The first four experiments are rendered nugatory by the absence of any means 
for destroying the ozone produced with the oxygen, which, as will be shown later, 
invariably accompanied the fluorine (see Column 9). 

No correction can be introduced into the figures for this source of error ; for the 
proportion of ozone to oxygen, produced under the conditions of the experiment, is 
not known, and the quantity of oxygen present is itself doubtful, since the nature of 
the reaction between ozone and mercury is not beyond dispute.* 

Any correction for ozone would reduce the value found for the index of fluorine. 

In the fifth and sixth experiments the measurements of the volumes of residual 
gases proved insufficiently accurate, and were complicated by the presence of ozone 
produced by the action of the fluorine on the solution of soda. 

In the last three experiments these sources of error had been eliminated, and we 
are forced to suppose that the method of absorbing the fluorine over mercury is open 
to some grave objection, possibly the formation of an oxyfluoride of mercury. It is 
certain that some source of error is to be sought in the process of absorption over 
mercury, since, in these experiments, the calculated values for the index of fluorine 
given in Column 10 are more discordant than those given in Column 4 for the 
observed refractivity of the mixture of gases. 

But, though this series did not give values sufficiently concordant to warrant the 
belief that the true index of fluorine was being measured, some important inferences 
could be drawn from the results. The number of values which ranged below the 
lowest figure obtained in Paris confirmed the opinion that, on that occasion, some 
other gas or gases were present. On the other hand, the absence of any very low 
value, in spite of the variety of methods employed, indicated that the refractivity of 
fluorine was to be sought in the neighbourhood of the figure 200, and was by no 
means so low as students of the refraction equivalents have surmised. 

But the most interesting point observed was the presence, in the residuals, of a 
larger proportion of oxygen than could be accounted for by the amount of air present. 
This was observed to be the case in all the experiments shown in Tables II. and III., 
as well as in others specially designed to test the point ;t and it was ultimately 
proved, beyond reasonable doubt, that the oxygen was produced by the intermittent 
electrolysis of traces of water in the electrolytic tube, and not by subsequent reactions. 
Our experience was that the proportions of oxygen and fluorine liberated were not 
sensibly altered by prolonging the experiment for two or three hours. 

Having established this fact, we were enabled to make dispositions for the series of 

* ANDREWS and TAIT, 'Phil. Trans.,' 1860, p. 114; SHENSTONE and CUNDALL, ' C. J.,' 51, p. 623; 
E. C. C. BALY, ' B.A. Reports,' 1897, p. 613. 

t It is hoped that the details of these experiments may be published on another occasion. 



ON THE REFKACTIVE INDEX OF GASEOUS FLUORINE. 



325 



experiments by which the index has, we believe, been measured with some approach 
to accuracy. 

Fig. 2 shows, in a diagrammatic form, the arrangement of the apparatus. A is 
the copper electrolytic tube, from the right side of which issues the fluorine. In 
order to prevent the escape of the vapour of hydrofluoric acid the exit tubes were 




Fig. 2. 

carried upwards, and surrounded by vessels, B 1( B 2 , containing alcohol, cooled to 
78 C. As a further precaution, the gas next passed through a length of 73 centims. 
of platinum tube immersed in a solution at the same temperature (C), and in many of 
the experiments a guard tube, filled with NaF, as recommended by M. MOISSAX, was 
added at the point F. The fact that the presence or absence of this salt did not 
appear to affect the refractivity of the mixture of gases is evidence that the other 
precautions were effectual. 

It was probable that some part of previously observed discrepancies arose from the 
presence of ozone produced when the oxygen was liberated ; and, in order to destroy 
this, the gases next passed through a spiral of platinum tube, 49 centims. in length, 
heated to from 250 to 300 C. (E). The bends, D and F, were immersed in iced 
water to prevent conduction of heat from the spirals to the condenser on one side and 
the refractometer tube on the other. 

The refractometer tube, H, was of platinum-iridium. 4578 centims. long and 
0'65 centim. in diameter. Its volume, with the leads, was 15 '01 cub. centims. Each 
end was furnished with a collar of platinum 0'25 centim. broad. The plates with 
which the ends were closed were of fluor spar, and were secured to the tube by a 
shoulder of shellac, melted round the outside of the circumference of the collar, so as 
to be as far as possible from the fluorine within. Thus, after leaving the electrolytic 
tube, the fluorine was never in contact with anything but platinum and fluor spar. 

The plan adopted for measuring the volume of fluorine present was to allow it to 



326 MESSES. C. CUTHBERTSON AND E. B. K. PRIDE AUX 

combine with an element whose fluoride was a solid (lead was chosen), measuring 
the contraction of volume so produced by means of mercury manometers which were, 
however, kept as far as possible from the fluorine by a column of air. 

In the figure, Lj and L 2 are graduated glass tubes of the same bore, having, at 
their upper extremities, narrow tubes filled with dry lead filings, K a , K 2 , and 
terminating in platinum tubes, Pj, P 2 , which fitted the leads of the refractometer 
tube. These closed burettes were connected with open movable burettes, Mj, M 2 , 
also of equal bore, which were joined by a wire passing over a pulley. One of the 
burettes (L 2 ) was in connection with a graduated reservoir of mercury, R, provided 
with a tap, and all were filled, to the proper point, with dry mercury. 

When the air in the refractometer tube had been displaced by the gaseous products 
of electrolysis as completely as possible, and the number of bands which had crossed 
the field had been noted, the entry tube was disconnected, and the two tubes 
P!, P 2 rapidly connected with the system of burettes, the junctions being made air- 
tight by immersing them in mercury. The burette M 2 was then raised slowly, while 
M 1; being connected by a pulley, fell by an equal amount. The mercury in LI, L 2 
followed the motion of that in their respective companions, and the effect was to push 
the contents of the refractometer tube into the glass tube at Kj, which was filled 
with lead filings, without appreciably altering the pressure, so as to avoid errors due 
to possible leaks. As the fluorine combined with the lead, there took place a 
diminution of the volume of gases in the closed space K 1; H, K 2 , which was indicated 
by a difference of level between the mercury in the closed and open burettes. As 
fast as this was observed, pressure was equalised by opening the tap Q and letting in 
mercury. By continuing and reversing this process the gases in the refractometer 
tube were pushed back and forward for about an hour. When no further change of 
levels could be detected it was assumed that all the fluorine present had been 
absorbed, and that the residual gases consisted of oxygen and nitrogen. The volume 
of fluorine was measured by observing the change of levels of the mercury in the 
two closed burettes, and the measurement checked by reading the change of level in 
the reservoir R. 

The amount of oxygen present was found by taking a sample of the total residual 
gases in the closed system and burning it with phosphorus. The residue was also 
tested for SiF 4 , and, finally, was shown by its index and spectrum to be nitrogen. 

From these data the index of fluorine could be found. But as the calculation is 
rather long, a specimen is given below, the figures being those actually observed in 
the third experiment given in Table III. 



ON THE REFRACTIVE INDEX OF GASEOUS FLUORINE. 327 

Barometer 741-5 millims. 
Thermometer (mean) 13 C. 

Length of the refractometer tube 45-78 centims. 

Number of bands which would cross the field for one atmosphere of air at normal 

temperature and pressure introduced into this tube 227- 6 

[NX = (p, - 1) x length of tube] 

Number of bands which would cross the field for one atmosphere of air at the 

temperature and pressure observed 212 

Number of bands observed to cross the field as air was displaced by gases 

produced by electrolysis 47 

Hence, by difference, number of bands which would cross the field for one 

atmosphere of these gases at the temperature and pressure of the day . . . 165 

Therefore the refractivity of the mixture of gases in the tube (air = 293) is 

2-ff* 293 = 228 

Volume of the refractometer tube and leads containing this mixture of gases . . 15-01 ciil>. centims. 

Volume of the gas absorbed by the lead filings 9 04 

Hence, by difference, the volume of gases in the refractometer tube and leads 

which are not fluorine (tube residuals) is 5-97 

Determination of the proportion of oxygen in the tube residuals from analysis of the contents of the 
burettes and refractometer tube (K b HK 2 ) after the experiment (total residuals) : 

Volume of total residuals 43-62 cub. centims. 

Volume of tube residuals 5-97 

Hence, by difference, volume of air was 37 65 

A sample of the total residuals contained 25 per cent, of oxygen. 
Therefore the whole contains, of oxygen, 

OK 

f^x43-62 = 10 . 90 

Of this amount the 37 '66 cub. centims. of air contain, of oxygen, 

20-9 



100 



x37-66 . . . 7-90 



And the difference between this and the whole quantity of oxygen found (10'9) is 3-00 

Hence the refractometer tube, at the moment when its contents gave a refractivity of 228, held 

Fluorine 9-04 cub. centims. 

Oxygen 3-00 

Nitrogen 2-97 

15-01 

Now, the refractivity of the mixture, multiplied by its volume, is equal to the sum of the refractivities of 
its constituents multiplied respectively by their volumes. 

Taking the refractivity of oxygen as 270 and that of nitrogen as 297, the refractivity of fluorine is given 
by the equation 

15-01x228 = 
whence 



328 



MESSES. C. CUTHBERTSON AND E. B. R. PRIDEAUX 



The following table shows the results obtained by this method. With the exception 
of the second experiment, which was discordant, probably owing to the presence of a 
slight leak afterwards detected, the coincidence is as close as we can hope to attain, 
having regard to the difficulties of the inquiry. 

We believe that the refractivity of fluorine for the D line lies in the neighbourhood 
of 195, most probably within 2 per cent, of that number. 

TABLE III. Refractive Index of Gaseous Fluorine. 



1. 


2. 


3. 


4. 


5. 


6. 


7. 


8. 


9. 


Num- 
ber. 


Date. 


Refrac- 
tivity of 
mixed 


Volume 
of tube. 


Volume 
of 
fluorine 


Volume 
of 
oxygen 


Volume 
of 
nitrogen 


Refrac- 
tivity of 
fluorine. 


Remarks. 






gases. 




present. 


present. 


present. 












cub. 


cub. 


cub. 


cub. 












centims. 


centims. 


centims. 


centims. 






1 


February 9,1905 


237 


15-01 


7-45 5-32 


2-24 195 




2 


18, 


225 


15-01 


8-40 2-43 


4-17 177 


A slight leak was 
















detected, after 


















the experiment. 


3 


D 28, 


228 


15-01 


9-04 


3-02 


2-95 


192 




4 


28, 


227 


15-01 


9-62 


2-25 


3-14 


194 




5 


March 10, 


236 


15-01 


8-4 


3-37 


3-24 


198J 


The glass tube KI 


















(fig. 2) holding 


















lead filings was 


















replaced by a 


















copper tube, to 


















diminish the 


















chance of ob- 


















taining SiF 4 . 


Mean of 1, 3, 4, and 5 . . . 195 




Index of gaseous fluorine 1-000195. 





The principal difficulties and sources of error involved in the method are as 
follows : 

(1) In disconnecting the refractometer tube and connecting with the measuring 

apparatus a few seconds are spent, and a small proportion of the contents of 
the tube may be lost by diffusion. To minimise this the leads were made 
about 20 centims. long, of platinum tube of less than 2 millims. bore. 

(2) The volume of fluorine present is measured by contraction during the com- 

bination of the fluorine with the lead filings. The success of the method, 
therefore, depends absolutely on the assumption that no gaseous compounds 
are formed, or that if formed (e.g., SiF 4 ) they are allowed for : and, secondly, 
on the absence of leaks. 



ON THE REFRACTIVE INDEX OF GASEOUS FLUORINE. 329 

These dangers were met by reducing the quantity of glass used as tar as 
possible, bringing the lead filings into immediate contact with the exits oi 
the refractometer tube, drying the whole with scrupulous care, and, finally, by 
testing the residuals for silicon fluoride. This test was carried out in three 
cases and only in one of these was a minute quantity of SiF 4 found (0*3 cub. 
centim.), which did not affect the index by more than one or two units. 

(3) The presence of ozone in the refractometer tube, especially if afterwards 

disintegrated, would introduce a serious error. The device employed to 
obviate this is described above. 

(4) Owing to the form of the apparatus it was not possible to isolate the tube 

residuals and measure their index directly, and their volume was so small, in 
comparison with that of the total residuals, that it would have been unsafe to 
calculate the refractivity of the former from that of the latter, even after the 
most careful measurements. It was necessary, therefore, to calculate the 
value of the refractivity of the tube residuals from their composition, 
ascertained by the analysis given above. But the calculation was confirmed 
by comparison with the figures given in the preceding series of experiments 
when the residuals were collected undiluted with air. Table II. shows that, 
in that series, the index lay, in nearly every case, between those of oxygen 
and nitrogen. 

It will be observed that the result given here rests on the assumption that the 
density of gaseous fluorine is 1'319 (air = 1) ; i.e.. that the molecule is diatomic under 
normal conditions. M. MOISSAN has twice measured this important constant. On the 
first occasion, in 1889, he obtained four concordant values,* 1'2G4, 1'2G2, 1'2G5, 1'270, 
the mean of which was 1'265, and he thence inferred that the gas contained a small 
proportion of molecules of Fj. f 

In 1904 a second series of experiments, in glass bulbs, gave values of 1/298, 1'319, 
I '313, 1'312, of which the mean is 1'310, a figure very nearly identical with the 
value assumed. We have accepted this later determination, which was made with 
the precautions dictated by many additional years of experience, and is supported by 
a priori probability. 

In a recent paper by Mr. CUTHBERTSON,^ it was shown that, in four groups of 
elements, the refractivities of the different members of the same group are related in 
the ratios of small integers, and it was pointed out that, if this coincidence were not 
due to chance, the refractivity of fluorine should bear to that of chlorine the ratio of 
one to four, as those of nitrogen, oxygen, and neon do to phosphorus, sulphur, and 
argon respectively. 

* 'Le Fluor,' p. 87; 'Ann. de Chimie et de Physique,' vol. 25, 1892, p. 131; 'C. R., ! vol. 109, 1889, 
p. 863. 

t 'C. R.,' vol. 138, p. 729 (1904). 

t 'Phil. Trans./ A, vol. 204, p. 323, 1905, 

VOL. CCV. A. 2 U 



330 



MESSRS. C. CUTHBERTSON AND E. B. R. PRIDEAUX 



This prediction has been verified. The refractivity of chlorine for sodium light is 
generally accepted to be 768, or 4x192. That which is now found for fluorine 
is 195. 

Table IV. shows the exact ratios experimentally obtained in all cases. The indices 
were determined, in the case of the inert gases for white light, in that of iodine for 
the red and the violet. In all other cases the measurements are for sodium light. 

It will be seen that, except in the case of the anomalous red rays in iodine, the 
discrepancies between the ratios actually found and those of integers do not exceed 
3 '2 per cent. A discussion of the possible causes of these discrepancies will be found 
in Mr. CUTHBERT.SOX'S paper. 

The element chosen as standard in each group is indicated by an asterisk, and, to 
avoid doubling all the other figures, the ratio of helium is taken as one half. 



TABLE IV. 



Elements. 


Reflectivities 
observed. 


Ratios in each 
group. 


Observer*. 










Helium 


72-6 


0-511 


RAMSAY and TRAVERS. 


Neon 


137-4 


968 


> 


* Argon 
Krypton . . . 
Xenon 


568 
850 
1 ;!78 


4 
5 986 
9 704 


" 


Fluorine 


195 


1-015 


CUTHBERTSON and PRIDEAUX. 


*Chlorine 


768 


4 


MASCART. 


Bromine 


1125 


5-859 





Iodine < 


1920V. 
2050 R, 


10 
10-68 


I HURTON. 


Nitrogen 
*Phosphorua 


297 
1197 


0-992 
4 


MASCART. 
CUTHBERTSON. 


Oxygen 
*Sulphur 


270 
1101 


0-981 
4 


MASCART. 
CUTHBERTSON. 



With the addition of fluorine the table given in the paper quoted above, showing 
the refract ivities of all the elements whose index has been measured in the gaseous 
state, now stands as follows. A few additional elements are put down to suggest the 
framework of the periodic system, and the refract ivities are rounded off. 



ON THE KEFKACTIVE INDEX OF GASEOUS FLUORINE. 



331 



TABLE V. Relative Refractivities of some of the Elements. 



H 
139 


He 

139 x| 


Li 


Be B N F No 
297x1 270x1 192x1 139x1 


Na 





P S CI A 

297x4 270x4 192x4 139x4 


K 





Bi KJ 

192 x (i 139 x (i 

| 


Rb 





I X 

192x10 139x10 


Cs 





> | 





Hg 

1857 


1 



We have pleasure in expressing our thanks to Sir WILUA.M RAMSAY and to 
Professor TROUTON for assistance throughout the research, to M. MOISSAN for his 
kindness in supplying the fluorine used in the first series of experiments, and to the 
Iloyal Society for grants in aid of the expense incurred in the research. 



2 u 



[ 333 ] 



X. Modified Apparatus for the Measurement of Colour and if* Application to 
tin- Determination of the Colour Sensations. 

Ht, Sn- WILUAM I.K W. ABXEY, K.C.K., f'.It.S. 

Received April 17, Head May 18, 1905. 

PART 1. 
(I.) Introductory. 

IN a paper contributed to the ' Phil. Trans.' in 1.899 on Colour Vision, the colour 
sensations in terms of luminosity were given in detail. Since that date a large part 
of the leisure which 1 could command outside my official duties has been occupied in 
revising the measures there given. To effect this revision, a modification of the 
apparatus I previously employed was carried out. Some slight alteration in the 
sensation curves was the result, and. though small, ought to be recorded. 

The principal alteration that lias to be made is in the amount of what may be 
called "inherent white" which exists in the spectrum colours. The white is due, 
at all events in part, to the overlapping of the three sensations. It will in the first 
instance lie necessary to describe the change that has been made in the colour-patch 
apparatus with which my previous measures had been made, since a good deal of the 
alteration in the blue sensation curve between X. 5000 and X 5100 is dependent on it. 

(2.) The Colour-patch Apparatus. 

The colour-patch apparatus is now arranged to enable two spectra formed by the 
same source of light to be used either separately or together. This arrangement 
allows a comparison of any differing mixtures of spectrum colours to be made, and 
it also allows the addition of any desired quantity of white light to the colours 
formed by the aid of either of the two spectra, 

In the original apparatus the intensity of the white light used for comparison with 
the colours varied with the intensity of the spectrum. The mode adopted to secure 
this result was to use the light reflected from the first surface of the first of the two 
prisms used in forming the spectrum. The beam of white light so obtained was 
reflected by a mirror on to the screen, on which the patch of colour was thrown. 
In the modified apparatus this principle of reflection has been still further utilized. 
The white light is used as before to form the spectrum to the comparison light, but, 
in addition, the light, after passing through the two prisms, passes through a half- 

VOL. ccv. A 396. 17.11.05 



334 SIR AV. DE W. ABNEY : MODIFIED APPARATUS FOR MEASUREMENT OF COLOUR 



silvered mirror, inclined at about 45 to the axis of the lens. The reflected beam is 
again reflected so as to pursue a course roughly parallel to the main spectrum, so that 
two similar spectra are placed side by side. The accompanying diagram will show 
the arrangement. 




55 



B 
\ 



Diagram of mo'litiud apparatus for the colour patch. 

As in the apparatus described in " ( 'olour Photometry," Part 111. (' Phil. Trans.,' A, 
L892), K is the soui'ce of light used outside a darkened room, LI, L> are lenses 
throwing an image of the source of light on the slit S, of the collimator C. TJie 
parallel beam passes through the prisms I 1 ,, P., and is received on a colour-corrected 
photographic lens, L h of sufficient diameter to take in the whole of the light coming 
through the prisms. 

The lens forms a spectrum on a focussing screen at D,, which can be removed and 
slits S 2 placed in the image. L (i collects the colours and gives an image of the face of 
the prism P, on the screen B. When slits are placed at D u the image is of the mixed 
colours passing through them. 

Behind the lens L, is placed a semi-silvered mirror M ]; reflecting, as nearly as 
may be, the same amount of light as is transmitted through it. If the mirror be on 
a plate of glass with parallel sides, it should be as thin as possible, to avoid any 
serious mixture of colour in the second spectrum clue to 
the reflection of the unsilvered surface. If a plate be made 
up of two thin prisms, as in margin, with the surface AB 
of one of them silvered, the transmitted beam is not deviated, and the beams reflected 
from DB and AC are diverted and not used. 




AND ITS APPLICATION TO THE DETERMINATION OF COLOUR SENSATIONS. 335 

The reflection from the semi-silvered mirror M! falls on a silvered mirror, M 2 , which 
reflects the beam in such a direction that it falls on B, the image of the spectrum 
being thrown on D 2 , in which are slits, S 3 . The image of P, is thrown on B by the 
lens L.v A beam of white light is reflected from the face of P] by M : , (\vhich may be 
either a silvered mirror or plain) and is also focussed on B, so that we have the 
patches from both spectra and from the white light falling over one another on B. 
By means of rods correctly placed, a colour or colours from either spectrum can be 
isolated and be mixed with anv proportion of white by using sectors as shown. 
There are slides carrying the slits at D! and I) 2 , and to them are attached trans- 
parent scales, [n the case of 1)^ a beam of white light falls on the mirror M 5 , as 
shown, and passes through the transparent scale at "<," and a lens X throws a 
magnified image of the graduation on a distant white screen, on which a zero mark 
is drawn. This enables the transparent half-millimetre scale to be read to a tenth 
of that unit. In a similar way the scale at " <t " is magnified by X' by a beam of 
light falling on M,. When the scale readings are not required, the sources of light 
illuminating them are covered up. 

Again the small lenses A 1 and A" are mounted in a sliding arrangement and can be 
moved in front of lenses L., and L ti . When a sl.it is drawn in front of A 1 or A 1 ' the 
image of the aperture is magnified on a distant screen, carrying a scale, and the 
width of the slits can be accurately ascertained by noting on such scale the reading 
of the breadth (say) of -J- millim. width of slit. This is the instrument with which 
the following measures were made. 

(:j.) I* t/icri' <i 4t/i Xcitx'ttinii. in tin- Vinli-t .' 

As in my previous investigations, the red at the red lithium line was used as 
exciting only the red sensation, and the violet at X4100 was also employed as a 
.provisional sensation, since it excited only the blue and the red sensations. 

Since my last paper on the subject was published, Brucn, in his paper in the 
'Phil. Trans.' (B, vol. 191, 1899) has given it as his opinion that besides the red, 
blue, and green sensations there is a 4th sensation excited by the violet. Before 
using the violet as a provisional sensation, it became necessary to ascertain if this 
4th sensation really existed, and various experiments were made with this object. 
From the first I was sceptical as to the 4th colour sensation, as it appeared to 
me to be unnecessary, and was a departure from the simplicity with which nature 
usually works. Amongst the experiments tried was that of fatiguing one of my 
own eyes with strong red light, and by a simple artifice immediately afterwards 
viewing a patch of violet light, keeping the uufatigued eye closed. The violet 
became a bright blue, whilst to the unfatigued eye it was of its natural violet hue. 
Not satisfied with my own vision, 1 got several unbiased persons to repeat this 
experiment, and they invariably stated that the patch became blue. A red-blind 



33fi SIR W. DE W. ABXEY: MODIFIED APPARATUS FOR MEASUREMENT OF COLOUR 

person matched without any difficulty the blue lithium line* with the violet near H, 
though he described the former as rather paler than the latter, a description which the 
colour- vision theory indicates as probable. Using my two eyes, one fatigued and the 
other not, I endeavoured to obtain a measure of the amount of red sensation 
destroyed, but owing to the mixture of white in the blue the match was never 
perfect, as the fatigue passed away before the match was made, and when white was 
added to the blue, it too had lost part of its red, and the " fatigued " violet appeared 



too green. 



These experiments and others went to prove the absence of the 4th sensation, and 
if further proof were required, it would be found in the ease with which the violet, 
when white is added to it, can be matched with a mixture of red and blue near the 
blue lithium line. 1 have therefore felt justified in using the violet as a temporary 
sensation in all my measures, reducing it to its components of red and blue in my 
final results. 

(4.) Fi, ''ft! f'niiifs in flic Spectrum. 

Several points in the spectrum could be readily f'ouzid. Thus the complementary 
colour to the red in the blue-green is a fixed point, as is the complementary 
colour to the violet. The complementary colour to the blue (near the blue lithium 
line) is also known. For other preliminary details a reference should be made to my 
previous paper. 

(5.) DeteriuiiMtioti of the \Vhitc in f/ic Colour which only excites the Green 

Sensation u-ith \\'hite. 

In my previous investigations 1 was unable to match spectral orange to which 
white could be added with mixtures of red and the green, but had to use the light 
transmitted through a solution of bichromate of potash placed in the path of the 
white (reflected) beam as representing an orange. By a suitable arrangement white 
could be added to it, till the mixtures were of the same colour. A small quantity of 
white had then to be added to the spectral orange to match the colour and the 
bichromate solution. From the two amounts of white added, the amount of white 
necessary to add to the spectral orange in order for it to match the mixture of red 
and green was deduced. With the apparatus now employed the determination of the 
amount of white to be added to the orange was made direct. There was also an 
advantage in these direct determinations with the spectrum colour, as more than one 
shade of orange could be used as checks to one another. 

The results of the many measures made show that a slight correction has now to 
be made to my previous determination. 

* It will be noted further ou that the blue lithium excites only the blue sensation and that of white. 



AND ITS APPLICATION TO THE DETERMINATION OF COLOUR SENSATIONS. 337 

(6.) Amount of Blue Sensation in Yelloiv and Yellow-yreen. 

In reviewing my previous measures of the amount of blue sensation in the yellow 
and yellow-green of the spectrum, I was struck with the variation of results 
obtained on different occasions, and though every care was taken at the time, I am 
led to think that the amount of this sensation was under estimated, though at the 
most the quantity is but small. This part of the spectrum has occupied my 
attention for a considerable time, and the determination of the blue sensation in this 
region has been conducted on perfectly different lines to that formerly employed, 
which was to make an equation by mixing the colour under consideration with red 
and violet in sufficient quantities to form white, and then to equate it with the 
standard equation. The equations were formed, but uo great stress is laid on the 
correctness of the blue sensation found, but only on the correct proportion of red and 
green sensation. The corrected value of the blue sensation was found by the following- 
plan : 

Slits were placed in the red and green at the standard positions red Li and 
SSN 37 '5 (standard scale number) in the green and as good a match as possible was 
made by mixtures of the two colours with the intermediate spectral colours, to which 
a little white was added. The amount of white added was not considered, but only 
the white inherent in the green. This last was deducted from the green and the 
percentage of red and green sensations in each colour calciilated without taking into 
account the white which was due to the presence of the blue sensation. From the 
equations were obtained the percentage of red and green when the white present in 
each colour -was included, and by the last measiires the percentage of red and green 
when such white was excluded. From these different percentages it was easy to 
calculate the amount of blue sensation present, for it only exists in the '' inherent 
white." On subsequently considering the sensation curves of equal stimulation as 
given by KCENIG and myself, my attention was called to the fact that at the place 
where the red and blue curves cut a large and very sudden increase of white inherent 
in the colour should be seen, so large indeed that it would never escape notice. The 
colour at that point ought to be much paler than colours close to it, but such is not 
the case. The new measures show that there is no sudden rise in the amount ot 
white present in any colour, and that the maximum of white is at SSN (standard 
scale number) 43 (X 5427) and not at 37'5 (X 5150). This point will be referred to 
later. 

(7.) Measures from the Blue-green to the Violet. 

The measures taken from the blue-green to the violet were made by the same 
method as described in the paper above mentioned, but the process was much 
simplified. The colour whose percentage composition had to be measured was isolated 
by a slit placed in one spectrum, and a slit in the other spectrum moved till a 

VOL. ccv. A. 2 x 



838 SIR W. DE W. ABNEY : MODIFIED APPARATUS FOR MEASUREMENT OF COLOUR 

complementary colour was found which, when mixed with the former, gave a match 
to white. The luminosity of each was taken separately when the match was 
complete. The composition of the part of the spectrum from the yellow to orange 
was already known, and the complementary colour found was converted into the 
percentage components of red and green. This enabled an equation in two standard 
colours and the unknown colour to be formed. When equated to the standard 
equation, the percentage composition of the last was found. When the colours 
in one spectrum approach the violet, the movement of the scale in the other 
spectrum to find the complementary colours is very small, and the magnified scale, 
formed as described, was of great assistance, since a vernier could be used when 
required. 

(8.) The Composition of the Violet. 

This remains as given in my previous paper of 1899. Many measures were made 
in this region of the spectrum, and the percentage of red to blue remains as before. 
The following are some of the principal measures : 

(9.) Inherent White Light in SSN 37 '5. 

To find the amount of inherent white in SSN (standard scale number) 37 '5. 
Taking an orange below D at SSN 50'2, it is found that in luminosities 

RS. 37-5. Orange. White. 
41 + 55 = 57 + 39. 

As there is no white in RS (red sensation), it follows that the 39 white is in 

55 (37'5), or that the 

Orange. RS. GS. 

57 = 41 + 16, 

and that there is |f of GS (green sensation) in 55 (37 - 5); that is, there is 29'5 per 
cent, of GS in (37 '5). 

Taking another orange near D at SSN 50 '05, it was found that 

RS. (37-5.) Orange. White. 

487 + 45-8 = 63 + 31'5, 
as before 

RS. GS. 

487 + 14-3 = 63. 

That is to say, there is 31 '2 per cent, of GS in (37'5). Other measures, and they 
were many, gave 

31 per cent., 3T8 per cent., 30'8 per cent., 29'8 per cent, 32'4 per cent., &c., 

and the mean gave 31 per cent, (very closely) of green sensation in the colour, and 
this number was adopted. 



AND ITS APPLICATION TO THE DETERMINATION OF COLOUR SENSATIONS. 339 

(10.) The Standard Equation. 

Four separate series of 50 equations each were made with slits at the red lithium 
line (37 '5) and (4) in the violet. The mean of each series gave the following results, 
using 31 per cent, of GS in (37'5) : 

RS. GS. V. White. 
68-48 + 30-16 + 1-36 = 100 
6818 + 30-50 + 1-32 = 100 
68-62 + 29-98 + 1-45 = 100 
68-44 + 30-17 + 1-39 = 100. 

The mean taken to one place of decimals gave 

RS. GS. V. W. 

68-4 + 30-2 + 1-4 = 100, 

and this equation was adopted as the standard equation for white. It will be noticed 
that this is somewhat different to the equation given in the former paper, but this 
is accounted for by the fact that the white of the comparison lights in the two 
cases are not quite identical, selective absorption by the glass used for reflection 
being far greater in the former measures than in the latter. The percentage of white 
in (37 '5) also differs. 

(11.) Red and Green Sensations from SSN's 58 to 49. 

The red and green sensations in this part of the spectrum were determined by 
placing one slit in the red lithium colour and another in the yellow-orange of one 
spectrum, and matching the intermediate colours thrown on the screen from the second 
spectrum. The composition of the yellows and orange used had been previously 
determined by mixing the colour of the red lithium with (37 '5) SSN : 

SSN. RS. GS. SSN. RS. GS. 

56-2 =95-6+ 4-4 56 = 96"5 + 3'5 

55-1 =92-6+ 7-4 55 = 93'!+ 6'9 

54-05 = 90 +10-0 54 = 90-5+ 9'5 

*54 =90-6+ 9-4 *54 = 90'6+ 9'4 

5275 = 86-8 + 13-2 52 = 84'2 + 15'8 

*52'6 =86 +14-0 *52 = 83-9 + 16-1 

51-6 = 80 +20-0 51 = 78-7 + 21-3 

*51'6 =80-2 + 19-8 *51 = 78-9 + 21-1 

50-9 = 79-3 + 207 50 = 75-0 + 25'! 

50-65 = 78-2 + 21-8 49 = 70'0 + 30'0 
*50'55 = 78 +22 
*497 = 75-7 + 24-3 
*49'3 = 73-6 + 26-4 

49-25 = 7T5 + 28-5 

The numbers marked * were taken with a slit at D, the others at 49'0 SSN. 

2x2 



340 SIR W. DE W. ABNEY: MODIFIED APPARATUS FOR MEASUREMENT OF COLOUR 

As special accuracy was necessary between SSN's 48 to 50, a large series ot 
measures was taken at this part of the spectrum. This necessity arose from the fact 
that a great part of the complementary colours between the greenish-blue and the 
violet lay in this part of the spectrum, ami their composition could only be accurately 
determined when the exact percentage of RS and GS was known. 

(12.) Red and Green Sensations from SSN's 49 to 37'5. 

The equations were formed, as stated before, in the ordinary manner, keeping the 
slits in the red and violet at the standard places and altering the position of the 
green slit. 

As an example, the value of SSN 45"8 was found as follows : 

RS. (45-8.) V. 

38-8 + 16-8 + 2-03 = White, 
or 

RS. 45-8. V. W. 

18-6 + 80-4 + 1 = 100, 
but 

RS. GS. V. W. 

68 -4 + 30 '2 + 1-4 = 100 (standard equation), 

.L 1 L* ' 

therefore 

45-8. RS. GS. V. 

LOO = 6T9 + 37-6 + -5. 
Similarly SSN's (40'5), (43), and (47 '5) were found 

(40-5.) RS. GS. V. 
100 = 5 1-68 + 47 -49 + '83. 

(43.) RS. GS. V. 
100 = 56-9 +42-5 +'60. 

(47-5.) RS. GS. V. 
100 = 66-20 + 33-5 +'30. 

The more accurate values of the violet were determined as described by matching 
the intermediate colours between SSN's 49 and (37 '5) of one spectrum by mixtures of 
these standard colours. Using luminosities, we get 

SSN. R. G. (37-5.) 
38 = 2-62 + 97-38 
40= 9-66 + 90-34 
42 = 17-16 + 82-84 
44 = 24-45 + 75-55 
46 = 31-31+68-69 
48 = 39-41 + 60-59. 



AND ITS APPLICATION TO THE DETERMINATION OF COLOUR SENSATIONS. 341 

Deducting 69 per cent, of white from the green (SSN 37 - 5), we get the following 
R and G sensations in luminosities : 

TABLE I. 

SSN. RS. GS. 
38 = 8 +92 
40 = 257 + 74-3 
42 = 40-1 + 59-9 
44 = 51-1 + 48-9 
46 = 59-2 + 40-8 
48 = 67-1 + 32-0. 

From the plotted curves of the red sensations and green sensations at this part of 
the spectrum we get the following figures : 

TABLE II. 

SSN. RS. GS. 
38 = 47-9 + 51-2 
40 = 51-0 + 48-5 
42 = 54-9 + 44-7 
44 = 57-7 + 41-9 
46 = G2 +37-6 
48 = 67 +32-9. 

Any slight corrections due to alterations found in the violet were made in the green 
sensations. The violet was calculated from Tahle I. and Table II. as follows : 
There is a certain quantity of red sensation and of green sensation which with the 
violet forms white. From the standard equation we know that the luminosity of the 
red sensation is 2*265 times larger than the green sensation and 49 times larger 
than the violet in the white. If x be the factor of red in Table I. (which is only due 
to the excess of red beyond that required to form white), then the same factor must 
be used with the green. The red sensation in Table II. (which takes into account 
the white present in the colour) must have deducted from it the red of Table II. x x, 
and the resulting amount must equal the green in Table II. less the green in 
Table I. x a; and multiplied by f|4f or 2 '26 5. 

Let R be the red in Table I., R! the red in Table II., G the gi-een in Table I., and 
GI the green in Table II. Then 

R-.-eR, = (G-xGJ 2-265. 

From this equation we derive x. When x is found, we have a known amount of 
red on the left-hand side of the equation, which is the amount which combines 



342 SIE W. DE W. ABNEY : MODIFIED APPAEATUS FOE MEASUEEMENT OF COLOUE 
with green and violet to form the white, and - gives us the amount of violet. 

4*7 

Take, as an example, SSN (42) : 

ES. ES. GS. GS. 

54'9-40-la; = (447-59'92a;) 2'265. 

From this we get 

, 54-9-40-1 x -484 - 

x = '484 and = '726, 

49 

the amount of violet present in SSN 42. 

The scale numbers in Tables I. and II. were thus treated and the violet as shown 
in Table III. was so obtained. 

(18.) Colour Sensation* in SSN (37'5). 

The amount of white light in (37 - 5) has already been determined as 69 per cent. 
It only remains to add this amount of white to the green in the standard equation 
and equate it when so altered to the standard equation. 

When the luminosity of the GS is increased by 69 per cent, the equation becomes 

ES. (37-5.) V. W. ES. GS. V. 

40'91-f 58'27 + '84 = 100, the standard equation being 68'4 + 30'2 + r4 = 100. 

These give us the composition of 

(37-5.) RS. GS. V. 

100 = 47-19 + 5T85+-96. 

(14.) Determination of SSN's from 36 to 12. 

The method described above was adopted to determine the SSN's 36 to 12. The 
following is an example : 

(54.) (34-9.) W. 

53'4 + 46-6 = 100 (j.), 

(54.) ES. GS. 

But 100 = 90-5 + 9-5 (ii.). 

From (ii.), (i.) becomes 

RS. GS. (34-9.) W. 
48-33 + 5-08 + 46-6 = 100. 

Equating with the standard equation we get 

(34-9.) ES. GS. V. 
100 = 43-07 + 53-93 + 3U 



AND ITS APPLICATION TO THE DETERMINATION OF COLOUR SENSATIONS. 348 

Another example may be given of SSN 25'5. The equation is 

(49-05.) (25-5.) 

96 + 4-0 = 100. 
RS. GS. 

In 49'05 there is 70'1 +29'9, and the equation becomes, after equating with the 
standard equation, 

(25 -5.) RS. GS. V. 
100 = 27-5 + 37-5 + 35. 

Similarly it was found that 

(27-1.) RS. GS V. (18-6.) RS. GS. V. 

100 = 30-8 + 45-9 + 23-3, 100 = H-3 + 7'3 + 81 "5, 

(23-7.) RS. GS. V. (15-5.) RS. OS. 

100 = -24 + 24 + 52, 100 = 4'6 + 2'l +93'3. 

Beyond SSN's 14 and 12 respectively, where the red and green sensations vanish, 
the violet alone remains, but having different intensities. 

(15.) Formation of the Sensation Curves. 

From the foregoing equations curves of violet-green sensation and red sensation 
were plotted, and any small irregularity was smoothed. The ordinates thus found 
are given in the following Table III., in Columns IV., V., and VI. 

Columns I., II., and III. represent (i) the standard scale numbers of the prismatic 
spectrum (the same as used in my previous paper), (ii) the wave-lengths, and (iii) the 
luminosity of the spectrum of the crater of the electric (arc) light as judged by the 
centre of the eye. 

Columns VII., VIII. , and IX. are the luminosities of the colours in terms of the 
red sensation (RS), the green sensation (GS), and the violet (V). These are obtained 
by multiplying IV., V., and VI. by Column III. and dividing by 100. 

In Columns X. , XI. , and XII. are given the percentage composition of the different 
rays in terms of RS, GS, and BS (the blue sensation). These are obtained by 
reducing the violet sensation to -ffa of its value in Column VI. (which is the 
percentage of blue which the violet contains), and adding i- - - of the violet to the 
red in Column IV. GS is the same in Columns V. and XI. 

Columns XIII., XIV., and XV. are the luminosities of RS, GS, and BS as contained 
in the different colours, and are obtained, as before, by multiplying XI., XII., and 
XIII. by the luminosities in Column III. and dividing by 100. Column XVI. is 
Column XIV. multiplied by 2 '3, and Column XVII. is Column XV. multiplied 
by 178. 



344 SIR W. DK W. ABNEY : MODIFIED APPARATUS FOR MEASUREMENT OF COLOUR 



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AND ITS APPLICATION TO THE DETERMINATION OF COLOUK SENSATIONS. 345 



The areas of the curves given by Columns XIII., XVI., and XVII. are equal, and 
represent equal stimuli of all three sensations. A mixture of the three colours, 
each being represented by ordinates of the same height, makes white. The points 
where the red and green curves cut the blue curve are the points in the spectrum 
which the green-blind and the red-blind match with white. 




5 10 15 ^0 Z5 30 35 40 45 50 55 60 

Fig. 2. Sensation curves having equal areas (equal ordinates at any poin*-- make white). 





^**. 



5?. 



SSr 



100 
90 

ao 

60 

so 

40 
30 
20 
JO 



35 40 

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45 



50 



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Fig. 3. Percentage composition in luminosities of red, green, and blue sensations of the spectrum colours. 
VOL. CCV. A. 2 Y 



346 SIR W. DE W. ABNEY : .MODIFIED APPARATUS FOR MEASUREMENT OF COLOUR 

(16.) Determination of Colour Sensations and White. 

The results given in Table III. are carried still further in Table IV. In it 
Column L, is as before, the standard scale number. Columns II., III., IV., V. are 

TABLE IV. 



I. 


II. III. IV. 


V. VI. VII. VIII. 


IX. 


X. XI. 






' 1 








Luminosity of sensation together 
with the white. 


Percentage composition of 
the sensations, white being 
deducted. 


Colour mixtures. 


SSN. 












RS. 


GS. 


BS. 


W. 


RS. 


GS. 


. BS. 


R. 


G. 


B. 


64 


2 








100 






100 








62 


2 








100 





=j_ 


100 








60 


7 


. 





100 





100 








58 


20-79 


21 





99 1 





97-2 


2-8 


56 


47-75 


2 25 





95-5 


4-5 





86-8 


13-2 





54 . 


72-40 


7-60 


. 


90-5 


9'5 





74-7 


25-3 





52 


80 64 


15-36 





84-2 15-8 





62 


38 





50 


75 


25 





75 25 





48-4 


51-6 





48 60 


29-5 





7-5 67-1 32-9 





38-7 


61-3 





46 38-2 


25-7 





23-1 59-9 


40-1 





31-5 


68-5 





44 22-5 


21-6 


_ _ 


30-9 51-1 


48-9 





24-3 


75-7 





42 


12-8 


18-2 





31-5 40-1 


59-9 





17-6 


82-4 





40 


5-8 


15-4 





28-8 27-4 


72-6 





10 


98 





38 


1-4 


11-4 





24-5 10-9 89-1 





3-5 96-5 





36 





8 


031 


16 99-6 


386 





99-87 


13 


34 





5-1 


OS8 


9 


98-31 i 1-69 





99-47 


53 


32 





3-2 


125 


5-2 





96-24 : 3-76 


98-09 


1-91 


30 





2-12 


155 


3-43 


_, 


93-18 6-82 


97-78 


2-22 


28 


. . 


1-33 


192 


2-48 


87-37 12-63 


95-71 


4-29 


26 


* -53 


235 


2-03 


68-8 31-6 


87-56 


12-44 


94. 

tOTi 


03 


250 


1-66 





10-5 


89-5 





27-42 


72-58 


22 -43 


. 


245 


73 


15 





85 


15 





85 


20 -54 





235 


33 


69-7 


. 


30-3 


69-7 





30-3 


18 -51 





201 


15 


71-8 





28-2 


72 





28 


16 -49 





180 


03 


73-1 


26-9 


72 





28 


14 -39 


. 


154 





72 


28 


72 





28 


12 -334 





126 





72 


28 72 





28 


10 -253 





098 





72 


28 


72 





28 


8 -187 





073 





72 


28 


72 





28 


6 -130 





051 





72 


28 


72 





28 


4 


101 





039 





72 




28 


72 





28 


n 


072 





028 





72 





28 


72 





28 





057 





022 





72 




28 


72 





28 


Areas . 


450 


192 


2-53 


187 





RS, GS, BS, and (white) W. These are obtained from Columns XIII., XVI., and 
XVII. of Table III. From SSN (standard scale number) 64 to 49 no white is present 



AND ITS APPLICATION TO THE DETERMINATION OF COLOUR SENSATIONS. 347 

in the colours, but at 48 some small quantity of white is shown to exist, and it is 
found to SSN 16. Taking SSN (40) as an example, in Table III. this colour has for 
its components in the columns showing equal stimuli 

RS. GS x 2-3. BS x 178. 
25-80, 55-40, 20. 

As equal ordinates make white, the smallest ordinate, 20 in that case, is deducted 

from the other two and we have 

RS. GS x 2-3. 

5-80 and 3 5 '40. 



35-40 
2-3 



or 



Thus after deducting 28 '8 of white, the amount of ES is 5 '8 and of GS 

15'4, so that the colour at SSN (40) is given by the equation 

ES. GS. W. SSN (40). 
5-8 + 15-4 + 28-8 = 50. 

In the same way the equations to the other colours of the different SN's were found, 
and fig. 4 gives the curves of RS, GS, BS, and W. It will be seen that all the 



90 



80 



70 



fiO 



SO 






W 



30 



0.S (too r, 



V 



X 



20 



10 



20 




\ 



30 



35 

SCALE of 



45 



so 



55 



60 



Fig. 4. Luminosity curves of red, green, blue and white sensations of the prismatic spectrum of the 

crater (positive pole) of the arc light. 

curves are smooth, and not one is abrupt, which is the case where the old numbers in 
my paper of 1898 for the BS are treated in the same way, more especially in the 
green and white curves. 

Columns VI. , VII., and VIII., Table IV., give the percentage composition in terms 
of RS and GS, GS and BS, and of RS and BS of the different colours. These 
columns are useful when we are considering the accurate calculation of the colours of 
pigments either reflected or transmitted. 

2 y 2 



348 SIR W. DE W. ABNEY : MODIFIED APPARATUS FOR MEASUREMENT OF COLOUR 

Columns IX., X.,and XT. give the percentage composition of the different colours of 
the spectrum in terms of the three colours which best represent the colour sensations 
when white is deducted from them, viz., red lithium, SSN 37 '5, and SSN 23 '2. 

In reference to this table it may be remarked that of the whole spectrum '225 is 
white and '775 colour. This shows that the white in the colours is by no means a 
negligible quantity. 

(17.) Significance of the Inherent White. 

In regarding the table, Column V., for white, it will be remarked that the maximum 
amount of white is near SSN (42). In ' Colour Photometry,' Part III. (' Phil. Trans.,' 
1892), it was shown that in this region the light disappeared last when the intensity 
was reduced. It was also shown that the maximum luminosity of a very feeble 
colourless spectrum was near this point, and in the concluding page of my last paper 
on the colour sensations, I pointed out that the presence of the fundamental sensation 
of light, which is white, must be taken into account in any theory of colour vision. 
The fact that in these slightly revised measures we get more than indications that 
white exists in the region where the fundamental sensation has been shown also to 
exist, leads one to believe that we are in some way separating this sensation from the 
three-colour sensations. What seems to confirm this view is that when a very bright 
spectrum, such as is given by sunlight, is measured, there is a tendency for the 
proportion of white in the region SSN's 48 to 16 to diminish. This is what we should 
expect to find, since fixed amplitude of wave colour vanishes at some, as also does the 
fundamental light at a lesser amplitude, be the spectrum feeble or brilliant. 

(18.) The Normal Spectrum Curves. 

Table V. gives the sensation curves for the normal spectrum, and is shown in the 
same manner as it was in my previously quoted paper. 



AND ITS APPLICATION TO THE DETERMINATION OF COLOUR SENSATIONS. 349 
TABLE V. Normal Spectrum. 



Wave- 
length. 


Spectrum 
lumi- 
nosity. 


Percentage composition. 


Luminosity. 


RS. 


GS. 


BS. 


RS. 


GS. 


BS. 


GS x 2-38. 


BSxl46. 


6800 


I 


100 






1 










G700 


6 


100 








C 














6600 


10 


99-7 


3 





9-97 


03 


. 


070 





6500 


17 


98-5 


1-5 





16-74 


26 





6 





6400 


26 


97 


30 


. 


25-22 


78 





1-9 





6300 


41 


95 


50 





38-95 


2-05 





4-9 





6200 


59 


92 


8 


. 


54-28 


4-72 





11-2 





6100 


75 


88-5 


11-5 





66-25 


8-75 





20-8 





6000 


85 


84 


16 





71-4 


13-60 





32-4 





5900 


93 


78-5 


21-5 





72-93 


20-70 





48-7 





5800 


99 


72 


28 





71-28 


27-72 





66 


_ 


5700 


100 


66-2 


33-8 


028 


66 '20 


33-80 


028 


80-4 


050 


5600 


95 


62-2 


37-7 


104 


59-09 


35-91 


099 


85-4 


145 


5500 


89 


58-5 


41-4 


1 50 


52-06 


36-84 


133 


87-8 


19-4 


5400 


80 


55-2 


44-6 


185 


44-96 


34-88 


148 


83-1 


21-6 


5300 


70 


52-7 


47-1 


215 


36-89 


32-97 -150 78-5 


21-9 


5200 


54 


49-5 


50-3 -243 


26-73 


27-16 -131 64-1 


19-1 


5100 


30 


46-5 


53-1 -400 13-95. 


15-93 -120 


37 8 


17-5 


5000 


18 


43-8 


55-3 


860 


7-88 


9-95 


155 


23-7 


22'6 


4900 


11 


42 


56 


2-00 


4-62 


6-16 


220 14-7 


32-1 


4800 


7-5 


43 


52-4 


4-6 


3-23 


3-93 


345 9-4 


50-3 


4700 


5 


50 


41-3 


8-7 


2-50 


2-06 


435 4-9 


63-5 


4600 


3-5 


62 


21-8 


16-2 


2-17 


76 


567 1-8 


82-7 


4500 


2-7 


72 


7-3 


21-7 


1-94 


20 


586 -5 


85-5 


4400 


2-1 


72 


2-2 


25-8 


1-51 


05 


542 -1 


79-1 


4300 


1-7 


72 





28 


1-22 





476 


69-5 


4200 


1-3 


72 





28 


94 





367 


53-6 


4100 


1 


72 





28 


72 





280 


40-9 


4000 


75 


72 





28 


54 





210 


30 '7 


3900 


50 


72 





28 


27 





140 


20-4 


3800 


25 


72 





28 


13 





070 


10-2 










1 1 






100 
90 
80 
70 
60 kj 



ff.s. 



\ 






/ 



V 

\ij 



2 



30 







10 



X 



4500 



5000 



5500 
LENGTHS. 



6000 



65CO 



6800 



SCAL OF 

Fig. 5. Percentage composition in luminosities of red, green, and blue sensations of the colours of 

the normal spectrum. 



.S50 SIR w. DE w. ABNPIY : MODIFIED APPARATUS FOR MEASUREMENT OF COLOUR 



90 



80 



\ 



z 



\ 



X 



I 



\ 



"5 

! 



X 



X 



\ 



\ 



20 



10 



\ 



4500 



5000 



5500 6000 

or WAVE tf/var#s 



6500 



Fig. 6. (Normal spectrum) Curves of equally stimulated red, green, and blue sensations to form white. 



PART II. 

(19.) A Colour Defined Inj a Ware-length, &c. 

In a note " On the Numerical Registration of Colour," which I communicated to 
the Royal Society ('Proceedings,' vol. 49, 1891), it was indicated that any colour 
could be accurately defined by a wave-length, its luminosity, and the percentage of 
white light that it contained. In Table III. we have a very ready means of stating 
all these with extreme accuracy. 

If the percentage of each colour of the spectrum which a coloured medium or a 
pigment transmits or reflects be known from measurement, then from Table III. we 
can find the wave-length, the luminosity, and the percentage of white light which 
the colour contains. 

(20.) Measurement of Spectrum Intensity. 

I have already described the method employed by myself in measuring the intensity 
of the light transmitted or reflected. Fig. 7 shows the plan. S is the slit moving in 




Fig. 7. 



AND ITS APPLICATION TO THE DETERMINATION OF COLOUR SENSATIONS. 351 

the spectrum, L the lens throwing the image of the face of the prism on the screen G. 
In the path of the ray X a plain glass mirror is inserted reflecting a proportion of the 
beam to a second silvered mirror M a , which in its turn reflects the beam Y to C. 
Sectors can be inserted in one or both of the beams X and Y. 

If the colour to be measured is that of a piece of (say) coloured glass, it is inserted 
at D in the path of the beam X ; or if it be a pigment whose colour has to be measured, 
it is placed at C, so that it is illuminated by X, and a white square placed adjacent to 
it is illuminated by Y, a rod R being placed in a proper position to throw two shadows 
touching each other at C. I have found that instead of using one plain mirror at M, 
it is better to have a bundle of glasses, so that the intensities of the beams X and Y 
are more equal than when a single glass is employed. 

The readings are made by equalizing the brightness of the illuminated shadows 
first with the colour in position and then without. The two measures give the 
percentage of light reflected or transmitted from the coloured medium or surface. 

(21.) Measurement of Emerald-green and Chrome-yellow. 

As examples of the way in which Table III. is to be used, the light reflected from 
emerald-green, Table VI., and from chrome-yellow, Table VII., has been tabulated. 

In both tables Column I. shows the standard scale numbers. 

In both tables Column II. the relative intensity of the light reflected from the 
colour compared with that reflected from a white surface. 

In both tables Columns III., IV., and V. are copied from X., XL, XII. , Table III. 

In both tables Columns VI., VII., and VIII. are III., IV., and V. multiplied by the 
intensities in Column II. 

The areas of the curves of RS, GS, and BS in VI. , VII., and VIII. for emerald- 
green are taken and found to be on an empiric scale (which is the same as that of 
the luminosity of the naked spectrum of the crater of the arc light), RS 202, GS 133, 
BS 1-418. 

GS and BS are multiplied by 2 '3 and 178 (the factors for making the sensation 
curves of equal area) respectively, and found to be 306 and 252 respectively. The 
lowest of the ordinates is RS 202. This must be deducted from GS x 2'3 and BS x 178, 
and we have as the remainders 104 and 50. These must be divided by 2 '3 and 178, 
and from these (which are 45'2 and '28) the percentages of GS and BS are calculated, 
and are found to be 99'38 and '62. This, from the diagram and from calculation, 
gives the dominant colour as SSN 35'64 or X 5070. 

The area of the spectrum curve is 830 on the same scale, and the sum of the three 
curves is 336. The luminosity of the emerald-green, when white is taken as 100, is 
Jrtt x 100, or 40'5. (This is the same as was made by direct measurement.) 

The amount of RS and GS and BS used to form the white is 290. The sum of the 
areas of the three curves is 336. The percentage of white is therefore f~f x 1 00, 



352 SIR W. DE W. ABNEY : MODIFIED APPARATUS FOR MEASUREMENT OF COLOUR 

or 86 '3. The amount of inherent white in SSN 35 '64 is 68 '5, so that there is 
38 per cent, more white in emerald-green than there is in SSN (35'64). 
Emerald-green is therefore represented by 

SSN 35-64. W. Emerald-green. 

62 + 38 = 100. Luminosity 40'5. 

Chrome-yellow was treated in the same manner. 



TABLE VI. Emerald-green Pigment. 



I. 


II. 


III. IV. V. 


VI. 


VII. 


VIII. 








t ! 












Intensity 


Composition of white 
in luminosity. 


Composition of green 
in luminosity. 




SSN. 


colour 










(white 


















100). 


RS. 


GS. 


BS. 


RS. 


GS. 


BS. 




64 


3-5 


5 








02 

f\n 








To find luminosity 


62 


3-5 


2 








07 










60 


3-5 


7 








24 








Sum of areas of green = 336. 


58 


4 


20-8 


2 





83 








Sum of areas of white = 830. 


56 


5 


47-75 


2-25 





2-39 


11 







54 


8 


72-4 


7-6 





5-79 


6 





Luminosity of emerald-green 


52 


14 


80-64 


15-36 





11-3 


2-16 







50 


28 75 


25 





21 


7 





= x 100 = 40-5. 


48 


42 65-16 


31-78 


039 


27-36 


13-34 


017 


830 


46 


53 ; 54-2 


32-7 


090 


28-73 


17-33 


047 


To find the amount of white and 


44 
42 


63 43-75 
71 | 34-61 


30-81 
27-75 


118 

122 


27 56 
24-57 


19-41 
19-7 


074 
086 


the dominant wave-length 


40 


74 25-8 


24-09 


112 


19-9 


17-83 


083 


RS = 202, 


38 


74 17-5 


18-43 


091 


12-95 


13-65 


067 


GS=133, 


36 
34 


73 11-09 
70 6-22 


12-83 
7-86 


101 
124 


8-10 
4-35 


9-34 
5-5 


074 

087 


BS= 1-418, 


32 


65 


3-58 


4-77 


145 


2-31 


3-12 


094 


GS x 2 3 = 306, 


30 


61 


2-45 


3-08 


174 


1-49 


1-84 


106 


BSxl78 = 252. 


28 


58 


1-78 


2-03 


202 


1-08 


1-2 


117 




26 


53 


1-41 


1-15 


243 


74 


61 


129 


Residue after forming white 


24 


46 


1-15 


53 


262 


51 


24 


121 


S06 - *>02 


22 


40 


91 


24 


247 


Sfi 


. -I 


.AQQ 


OVVJ ft \frnl A r* (\ f~i ci 
1 r) " IT ft 


20 


32 


77 


1 


234 


ou 

24 


03 


Vi/t7 

075 


2-3 


18 


27 


62 


04 


202 


18 


01 


054 


252-202 . oqps j 


16 


22 


51 


01 


18 


11 





04 


178 


14 


17 


39 





154 


07 





026 




12 


12 


33 





126 


04 





015 


Percentage of GS and BS 


10 


5 


25 





098 


01 


, 


005 


Emerald- 


8 


3-5 


19 





073 








002 


GS. BS. green. 


















99-33+ -62 = 100. 




Areas . 


202 


133 


1-418 


This is SSN 35-64 or A. 5070. 



AND ITS APPLICATION TO THE DETERMINATION OF COLOUR SENSATIONS. 353 



TABLE VII. Chrome-yellow Pigment. 



I. 


II. 


III. 


IV. 


V. VI. 


VII. 


VIII. 




Intensity 
of 


Composition of white in 
luminosities. 


Composition of yellow 
in luminosities. 




SSN. 


colour 










(white 
















100). 


RS, 


GS. 


ES. 


RS. GS. 


BS. 




64 


100 


5 




_ 


5 






To find luminosity 


62 


100 


2 







2 








60 


100 


7 








7 


. 





Sum of areas of yellow 682. 


58 


100 


20-8 


2 





20-8 


20 





Sum of areas of white = 830. 


56 

54 


100 
100 


47-75 
72-4 


2-25 
7-60 





47-75 
72-4 


2-25 
7-60 





Luminosity of yellow 


52 


100 


80-64 


15-36 





80-64 ' 15-36 





68 


50 


100 


75 25 





75 25 





= g2 x 100 = 82-2, 


48 


100 


65-16 ! 31-70 


039 65-16 . 31-70 


034 




46 


100 


54-2 '32-70 


090 54-20 32-70 


090 


white =100. 


44 
42 
40 


84 
62 
42 


43-75 30-81 -118 36 -75 25-88 
34-61 | 27-75 -122 21-46 17-20 
25-80 24-09 '112 ' 10-83 10-12 


099 
076 
047 


To find the white and dominant 
wave-length 


38 


26 


17-50 


18-43 -091 4-55 4-78 


024 


RS = 504, 


36 


19 


11-50 


12-83 -101 


2-11 2-44 


019 


GS=178, 


34 


16 


6-22 


7-86 


124 


1 1-26 


021 




32 


14 


3-58 


4-77 


145 


5 -67 


020 


BS 694, 


30 


12 


2-45 


3-08 


174 


29 37 


021 


GSx2-3 = 409, 


28 


11 


1-78 


2-03 


202 


19 


22 


022 


BSx 178=123. 


26 11 


1-41 


1-15 


243] 










24 


11 


1-15 


53 '262 








Residue after forming white 


22 
20 


11 
11 


91 

77 


24 -247 
10 '234 








504-123 = 381 RS 


18 


11 


62 


04 ' -202 








409-123 


16 


11 


51 


01 1 -180 






2-3 


14 

12 


11 
11 


39 
33 


154 . 
126 | 


76 -23 -216 


Percentage of RS to GS. 


10 


11 


25 -098 






RS. GS. Yellow. 


8 


11 


19 


075 






75-4 + 24-6 = 100. 


6 


11 


13 


052 








4 


11 


10 


039 




| 


Therefore chrome - yellou- is 


2 


11 


8 


028 








50 SSN, and contains 26 per 





11 


6 


022J 








cent, white. 


Areas . 


503-9 178 


694 





(22.) Principles of Three-colour Photography. 

At the present time the accurate determination of colour composition in terms of 
the three-colour sensations, of pigments, and transparent media, is of great practical 
importance. There is now a large business carried on in the production of prints by 
the three-colour process of photography, and up to the present time the colours 
produced are, with rare exceptions, wanting in truth, probably owing to screens of 

VOL. ccv. A. 2 z 



354 SIR W. DE W. ABNEY : MODIFIED APPAKATUS FOR MEASUREMENT OF COLOUR 

the wrong colours being used. In order to take the three negatives from which the 
prints are produced, it is necessary to place screens of different colours (reddish, 
greenish, and blue) in front of the sensitive plate in order to get distinctive images 
which will represent the three sensations in the three printings. As to the printing 
itself, nothing need be said in this communication, but I shall confine myself to the 
negatives alone. If the negatives are correct, three transparencies from them should 
give three images, which, if illuminated by the three colours which represent best 
the three sensations, and superposed, should give the true colours of nature. 

Where the three positives are each devoid of deposit at the same part of the image, 
the mixture of colours should give white, which means that in the negatives the 
deposits should be equally opaque. This is the starting point of the process. 

The deposit being without colour, the different parts of the three component 
negatives have to be such that the transparencies, when projected on a screen, allow 
so much of each coloured beam to pass as will give the natural colour by mixture. 
[It may be remarked that the negatives themselves, if illuminated with the three 
colours, and the images superposed, should show the complementary colours.] If 
there were a perfect photographic plate, there would not be much difficulty in 
calculating directly the colours for the three screens which should be used. As, 
however, no photographic plate is perfect in one sense, the proper exposing screens 
have to be ascertained by trial. It is useless to make such trials with the spectrum, and 
I have adopted a system which allows an accurate determination to be made by trial. 

(23.) The Pritidple on which a Colour Sensitometcr is Made. 

The principle I have employed, and which has been outlined before, is as follows : 
If we have to find a screen to take what we may call the red negative (i.e., one in 
which the opacities of deposit are proportional to the red components of the objects 
photographed), we may take a variety of pigments, each of which contains red, and 
utilize them for the purpose. Such pigments may show a diversity of luminosities, 
and the relative proportions of red, green, and blue will also be very different in each. 
If (say) squares of paper are covered with the pigments of different colours and 
photographed through almost any coloured screen we should be unable to say without 
measuring the different opacities of deposit whether the screen was correct or not. 
If, however, by some artifice we are able to make all the red components in each 
of the pigments identical, and then photograph them, it is evident that the only 
screen which would be correct would be that which would make the opacities of all 
the images of the different squares of colour the same. The mode I have adopted of 
reducing the intensities of pigments and making all the luminosities of red, green, or 
blue the same, is by making annuluses of the different pigments and filling up parts 
of them with black pigment (the amount of white light reflected from such black 
being measured and taken into account), and then rotating them round the centre of 
the disc on which they are fixed. 



AND ITS APPLICATION TO THE DETERMINATION OF COLOUR SENSATIONS. 355 

(24.) Practical Application of the above Principle. 

The method shown of ascertaining the composition of the colours in terms of the 
three sensations, and of ascertaining their luminosity, enables us to make an accurate 
determination of the amount of reduction which the various pigments should undergo. 
Suppose we wish, for instance, to make the red sensations in the yellow, the green, 
and the white the same, we should proceed as follows : 

The amount of red, green, and blue sensations in these three on the same empiric 
scale are 





RS. 

i 


GS. 


BS. 


White 


i 
I 
. . 571 


248 


3" ) C4 


Chrome-yellow . . . 
p]merald-green 


. . 503 
202 


178 
133 


694 
1 4 1 8 











If we reduce these sensations to colours, from Table IX. then we shall have for 
(say) the red component in white 342, in chrome-:yellow 284, and in emerald-green 79. 

In order to reduce all these to show equal red components, the centre of the disc 
would be occupied by emerald-green pigment. The chrome-yellow would have to 
be reduced to - 2 \ a 4 -, or '278 of its normal luminosity, so that '278 of 360, or 260 of 
the annulus, would have to be occupied by dead black. 

The white would have to be reduced to -g 7 ^, or '231 of its normal luminosity, so 
that 277 of the annulus would have to be occupied by dead black. 

If a green screen had to be obtained the green sensations reduced to green colour 
would be white 447, chrome-yellow 298, emerald-green 255. Then, as before, 
emerald-green would occupy the centre of the disc, and chrome-yellow would have 
to be reduced to fff, or '856 of its luminosity, and white to f I*, or '534 of its 
luminosity. 

The above will give an idea of the method to be adopted in making what I have 
called colour sensitometers. Examples have been given only with those pigments 
which have been considered in the foregoing pages ; but naturally there would be 
many other colours introduced in order, as far as possible, to imitate the spectrum 
colours. 



2 z 2 



[ 357 ] 



XI. The Pressure of Explosions. Experiments on Solid and Gaseous 
Explosives. Parts I. and II. 

By J. E. PETAVEL. 
Communicated by Professor ARTHUR SCHUSTER, F.R.S. 

Received August 18, Read November 16, 1905. 
[PLATE 21.] 



CONTENTS. 

Page 

Introduction . . .358 

PART I. 
METHODS AND APPARATUS. 

Explosive pressure gauges 359 

Maximum pressure gauge . . . 359 

Recording manometer 361 

Chronograph 364 

Explosion chambers 365 

Spherical explosion chamber 366 

Cylindrical enclosure 368 

Firing plug ; . . . . . 368 

Standard gauges 368 

Valves and connections . 369 

PART II. 
EXPERIMENTAL INVESTIGATION OF THE EXPLOSIVE PROPERTIES OF CORDITE. 

General shape of the curves 373 

Effect of the diameter of cordite 374 

Effect of the enclosure 379 

Relation of pressure to gravimetric density 384 

Distribution of the explosive 386 

APPENDIX : Tables of numerical results 390-398 

VOL. CCV. A 397. 30.12.05 



358 MR. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 

LIST OF FIGURES. 

No. 

1. Maximum pressure gauge . . . 

Recording manometer diagram . . . 

3. Recording manometer drawing . 363 

4. Chronograph camera 

5. Spherical explosion chamber 366 

6. Cylindrical explosion chamber 368 

7. Firing plug 

s. Valve and cone connections 370 

9. Effect of ignition by oxyhydrogen and by gunpowder compared ... . . 372 

10. Typical time pressure curve resulting from the explosion of cordite in a closed vessel . . . 373 

11. Variation of rate of explosion with the size of cordite used, gravimetric density 0- 10 . . . 374 

12. Variation of rate of explosion with the size of cordite used, gravimetric density 0-15. . . 375 

1 3. Effect of the gravimetric density and the diameter of the explosive on the time required to 

reach the maximum pressure 375 

1 4. Rate of rise of pressure for cordite of the smallest diameter 377 

15. Effect of the shape of the enclosure on the maximum pressure developed by cordite of large 

diameter 380 

16. Effect of the dimensions of the enclosure on the rate of cooling of the products of 

combustion 381 

17. Variation of maximum pressure with gravimetric density .... 384 

18. Diagram illustrating the action of the explosion wave which is set up when the explosive 

is unevenly distributed 386 

19. Variation in the rate of combustion and maximum pressure produced by a non-uniform 

distribution of the charge for cordite of 0-475 inch diameter 389 

20. Variation in the rate of combustion and maximum pressure produced by a non-uniform 

distribution of the charge for cordite of 0' 175 inch diameter 389 

INTRODUCTION. 

THE scientific treatment of this question may be said to date from the researches of 
Count RUMFORD who, at the end of the eighteenth century, devised the first 
apparatus by which explosive pressures could be estimated with some degree of 
approximation. 

During the past century the natural fascination of the subject, and the importance 
of the problems involved, attracted many of the ablest scientific minds. Several have 
made the study of explosions the object of their life work. 

In the short space available, an adequate historical epitome is unfortunately 
impossible. A mere enumeration of the names with which we shall most frequently 
have to deal must therefore suffice. 

Our knowledge of the behaviour of solid explosives is due principally to the 
brilliant work of NOBLE in this country, and of BERTH ELOT and VIEILLE abroad. 
With regard to explosive gaseous mixtures, the exhaustive work of LE CHATELIEB 
and MALLARD in Paris, of DIXON in Manchester, and CLERK in London, is familiar 
to all. 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 359 

At first sight it may appear to be over ambitious on the part of the author to 
attempt to add to the edifice built up by such able investigators. Closer consideration 
will, however, show that there is a gap in the structure ready to be filled by the small 
stone which he has quarried out. 

In the case of solid explosives, thanks to NOBLE'S crusher gauge, the actual 
maximum pressure attained can be accurately measured. The mechanism of the 
explosion itself and the rate at which the pressure rises from the moment of ignition 
need, however, further investigation. 

For gaseous explosives the same criticism holds true, more especially for mixtures 
which are highly compressed before they are fired. The first case has a bearing on 
all ballistic problems, the second provides some of the data necessary to the designers 
of the modern gas engine, and thus both are of considerable practical, as well as 
scientific importance. 



PART I. METHODS AND APPARATUS. 
Explosive Pressure Gauges. 

At the time this research was started, some six years ago, there was no instrument 
by means of which the variation of pressure during the course of such explosions 
could be satisfactorily recorded. Numerous attempts have been made, but without 
success, to reduce the moment of inertia of the existing types of recording manometers 
sufficiently to make them of service for this work. The natural period of oscillation, 
however, invariably proved to be too slow. In consequence, the curves traced out did 
not record the rise of pressure in the enclosure, but merely the vibrations set up in 
the mechanism of the gauge by the sudden shock to which it was subjected. To 
design a satisfactory instrument it was, therefore, necessary to start ab initio. 
Before, however, the work could be carried out, some further knowledge of the 
conditions prevailing during the explosion was necessary, and this more especially in 
the case of highly compressed gaseous mixtures, the behaviour of which was at the 
time practically unknown. 

Maximum Pressure Gauge. 

For this work a gauge was employed the construction of which will easily be 
understood from the drawing given in fig. 1. In principle the apparatus is the same 
as that used by BUNSEN, and consists of a piston closing an aperture in the explosion 
chamber, the piston lifting if the pressure of the explosion rises above the load for 
which it is set. 

To reduce the inertia to a minimum, the weights, used in BUNSEX'S apparatus, are 
replaced by a gaseous pressure. The moving part consists of a double-headed piston 



360 MR. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 

(P, p}, the smaller end of which (^>) is exposed to the force of the explosion, while 
the larger end (P) closes' a cylinder filled with gas at a known pressure. The piston, 




Fig. 1. Explosion gauge. (Maximum pressure indicator.) 

The gauge consists of a double-headed piston, P, p. The smaller head p is exposed to the pressure of the 
explosion, which is counterbalanced by a fixed gaseous pressure acting on the larger head P. The ratio 
of the two areas (and therefore of the two pressures when in balance) is fifty to one in the case of the 
gauge illustrated in this drawing. The lift of the piston is limited to about one hundredth of an inch, 
the distance of the stop B being adjusted by means of a fine screw. The piston on lifting closes an 
electric circuit and works an indicator. S is the stuffing box through which the stop B passes, C the 
cover of the cylinder in which the piston P works ; it is held clown by the nut N. G is the gas inlet 
by means of which the space E is connected to a source of supply of gas under pressure and to a 
gauge. K is the plug through which the electric connection to the insulated contact-piece H is made. 
To prevent back pressure, which might arise through leakage past either of the leathers, the space X 
is connected with the atmosphere by means of the vent V. 

on lifting, closes an electric circuit and works an indicator. To ensure rapid action, 
the travel of the piston is limited to about a hundredth of an inch. 

Two such instruments were constructed. The first, for pressures up to 100 
atmospheres, had a ratio of 4 to 1 ; in the second (shown in fig. 1), intended for use 
up to 1000 atmospheres, the ratio of the areas of the two sides of the piston was 
50 to 1. Fairly satisfactory measurements of the maximum pressure were obtained 
by means of this apparatus. 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 361 

With this instrument the work is very tedious, and no information is obtained as 
to the rate of combustion of the explosive. The experience gained during the course 
of the above preliminary investigation was, however, of the greatest use in the design 
of the final apparatus. 

Recording Manometer. 

The requirements for a reliable recording gauge are somewhat complex. In the 
case of gases, the explosive pressures to be dealt with range from 100 to 800 
atmospheres ; in the case of solid explosives it was desirable to extend the research 
to pressures of 2000 atmospheres, or above. The combustion of several gaseous 
mixtures is much more rapid than that of the fastest explosives used in ballistics, and 
the time period of a recorder designed for this work must, therefore, be exceptionally 
small. 

Before passing on to a description of the instrument it may be well to recall in a 
few words the law which governs the time period of vibrating bodies. 

If A represent the force required to produce unit deflection of the vibrating system, 
W the weight of the moving parts, the time period will be 



We have, therefore, two variables at our disposal, namely, the weight of the 
moving parts and the controlling force. The former must be made a minimum, the 
latter a maximum. 

In most instruments where a short period is desirable, the strains to which the 
parts are subjected are very small, and the desired result is obtained by decreasing 
the size of all moving parts, and using, wherever possible, materials of low density. 
This method is employed in the case of all oscillographs, telegraph recorders, 
phonograph receivers, galvanometers, &c. 

In the present case, the instrument having to withstand pressures of 20,000 or 
30,000 pounds per square inch, applied with extreme suddenness, strength becomes a 
condition of vital importance, and steel is the only material which will withstand the 
strain. We cannot, therefore, use materials of small density, neither can we reduce 
the dimensions of the moving parts below a certain limit. 

It is thus evident that we must have recourse to the second variable factor to 
secure the short time period which is necessary. As we have seen above, the 
controlling force brought into play per unit length of motion must be as great as 
possible. In other words, we must use the stiffest spring we can obtain. 

The stiffness of a spring will vary with the material of which it is made and with 
its shape, increasing as the shape approaches more nearly to that of a solid bar 
subjected to longitudinal strain. This bar can be made as short as may be desired 

VOL. CCV. A. 3 A 



362 MR J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 

and, in theory, the time period of the system is only limited by the density of the 
material and by its modulus of elasticity. 

In practice, however, the travel of the moving parts cannot be indefinitely 
decreased, for the deflections must remain of such dimensions as to be accurately 

measurable. 

The following diagram illustrates the application of the principles we have just 
established to the construction of a recording instrument (see fig. 2). 




Fig. 2. Diagram of recording manometer. 

A cylindrical groove is cut half through the walls of the enclosure. The upper part, 
P, of the cylinder thus obtained represents the piston of our indicator, and the lower 
portion, S, the spring. Under the pressure of the explosion the piston P will be 
forced outwards to an amount corresponding with the elastic compression of the 
material of which the spring is made. This motion is transmitted to the exterior by 
the rod R. 

The lever L, supporting the mirror, rests on the fulcrum F at 3 ; it is kept 
against the knife-edge 2 of R by the tension of the wire W. The wire W is of 
considerable length, and is stretched almost to its limit of elasticity. The lever L can, 
therefore, follow the small advance of the rod R without greatly diminishing the 
tension of the wire W. The mirror focuses a point source of light on to a rapidly 
revolving cylinder, thus recording on a magnified scale the motion of the piston P. 

It is not impossible that an indicator of this type would work in practice, but the 
deflection of the mirror, and, therefore, the scale of the records obtained, would be 
much too small. To increase the deflections, three modifications are necessary the 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 



363 



spring S must be made longer, the ratio of its cross-sectional area to that of the 
piston must be decreased, and the knife-edges 2 and 3 be brought closer together. 

In fig. 3 the design of the actual instrument is given, the lettering being the same 
as in the previous figure. 

By means of the thread U the gauge screws into the explosion chamber, the end 
C of the piston being flush with the inside surface. An air-tight joint is formed by 




w 



LJ LJ 



01 234 56789 10 

SCALE /N INCHES. 

Fig. 3. Recording manometer. 

the ring U on the manometer pressing against a flat ledge in the enclosure (see 
fig. 5, a). The end of the gauge from D to E is a good fit in the walls of the explosion 
chamber, and the joint is thus protected from the direct effect of the explosion. 

The spring S, about 5 inches in length, is tubular in shape. To prevent any 
buckling it is made to closely fit the cylinder, in which it is contained, at two places, 
e l and e 2 . The spring is fixed at the outer end Z, being held in place by the nut K ; 
at the inner end it is free and supports the piston P. The copper gas check used in 
the crusher gauge is replaced by a leather washer, attached to the piston by the 
screw C and to the fixed part of the gauge by the ring E. The end of the piston 
projects by about one-hundredth of an inch, and it can therefore move back, by this 
amount, without straining the leather. 

The mirror (not visible in the figure) is carried by the lever L. This lever is so 
designed that the knife-edges 1, 2 and 3 (see fig. 2) are in the same plane, it being at 
the same time possible to bring the knife-edges 2 and 3 within one-hundredth of an 
inch of each other, should so great an amplification be found necessary. Up to the 
present, however, the distance has not been decreased below one-sixteenth of an inch, 
the scale obtained with this distance being found sufficiently large. 

The actual working of this type of recorder has proved very satisfactory. Its time 
period is sufficiently small to allow records to be obtained not only of the curve of 
rise of pressure of the fastest cordite, but also of the rapid vibrations which modify 
the curve under certain conditions.* 

* Captain BRUCE KINGSMILL has proposed the application of this gauge to ballistic work with a view to 
" indicating " a gun in much the same manner as we now indicate a steam engine. This suggestion, which 
might lead to valuable results, has, as far as I am aware, not yet been carried out in practice. 

3 A 2 



364 



ME. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 



Chronograph. 

Owing to the high speed required, the chronograph used for this work had to be 
specially designed. It is unnecessary to go into all the details of its construction. 
The ordinary methods were used to measure the velocity of the rotating drum and to 
ensure the constancy of speed during the course of an experiment. 

When measuring the rise of pressure during an explosion, a linear speed of between 
100 and 1000 centims. per second was used. For measuring the fall of pressure 
during the cooling of the products of combustion the driving mechanism could be 
geared down to give a linear speed of 5 or 10 centims. per second. 

The drum of the chronograph can be easily detached and taken to the dark room, 
where the photographic film is wound on ; it is then placed in a light-tight box. As 
explained in connection with fig. 4, this box is so arranged that the drum can be 




SCALE IN INCHCS. 

Fig. 4. Chronograph camera. 

The drum D is shown fixed on the axle A of the chronograph. To remove the drum without exposing the 
film which is wound round it to the light, the camera is first moved a little to the right, causing the 
ring E on the camera to fit into the groove F of the drum. The brass tube G is next forced into the 
groove H ; its cover, C, can then be removed and the nut N unscrewed. The camera, with the drum 
firmly held in it, can now be detached from the chronograph (by sliding it to the right) and taken to 
the dark room, where the film is developed and replaced by a fresh one. 

fixed on to the axle of the chronograph in the full daylight without fogging the film. 
The box surrounding the revolving drum is pierced with a long and very narrow slit ; 
this, in turn, is covered by a shutter, which is lifted immediately before the explosive 
is fired and closed again a second later, after the photograph has been taken. 

Thanks to the above arrangement it is not necessary for the room in which the 
experiments are carried out to be absolutely dark. The mirror of the recorder is 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 365 

illuminated by a straight-filament incandescent lamp, the image of the filament being 
focused on to the slit of the chronograph camera, forming a straight streak of light 
perpendicular to the axis of rotation. The beam of light is deflected to an amount 
proportional at each instant to the pressure in the explosion chamber and, travelling 
along the slit of the camera in a direction parallel to the axis of rotation, traces 
out a curve on the photographic film. The ordinates of this curve represent the 
instantaneous pressures, the abscissae the times at which the said pressures existed. 

A low-voltage high-candle-power lamp is used to illuminate the mirror, the 
comparatively thick filament of such a lamp giving correspondingly more intense 
illumination. At the moment of firing, the lamp is switched for a few seconds on to 
twice its normal voltage, and thus the strongly actinic light required is produced. 

The recorder is calibrated by hydrostatic pressure before and after each set of 
experiments. 

Explosion Chambers. . 

It is well known that the shape of the enclosure has a considerable effect on the 
behaviour of the explosive during combustion. On the other hand, the ratio of the 
internal surface to the total volume of the chamber determines to a large extent the 
rate at which the pressure will subsequently fall. 

With a view of obtaining some further information on these questions, two 
explosion chambers were constructed having approximately the same volume, but 
differing largely in shape. The first, a sphere, offers the least possible cooling surface ; 
whereas the second, a long narrow cylinder, has a surface more than twice as great. 

One of the subjects of the research was to study the oscillations of pressure which 
are set up under certain conditions. In a long cylinder such oscillations are easily 
started, but in a small sphere the symmetrical shape and the short distance from wall 
to wall tend to equalise the pressure existing at each instant throughout the 
enclosure. Thus, in a spherical enclosure, the pressure rises usually without vibration 
and forms a smooth curve, the shape of which depends exclusively on the nature of 
the explosive used. In a long cylinder, however, the normal curve is modified by the 
distribution of the explosive, the method of firing, and various other factors. 

Before designing these chambers, the relative advantages of solid metal and wire 
winding were fully considered. The latter construction, if properly carried out, adds 
considerably to the ultimate strength. A system of winding suitable for a spherical 
enclosure is, however, not easy to devise, and this fact, together with the ever 
important consideration of cost, led to the adoption of solid walls. 

Mild steel was chosen as the material best suited to withstand the sudden impact 
of an explosion. The limit of elasticity, ultimate strength, and elongation of test 
pieces cut perpendicular to the direction of rolling were carefully determined before 
the forgings were machined. 



36(5 



ME. J. E. PETAVEL ON THE PRESSUEE OF EXPLOSIONS. 
Spherical Explosion Chamber. 



The first explosion chamber is a nearly perfect sphere, 4 inches in diameter (see 
fig. 5). The measurements made in a plane passing through the axis of rotation 




Fig. 5. Spherical enclosure. 

The recording gauge screws in at A, the firing plug at B, and two valves at C and D respectively. The 
spigots, which are turned on the forging at either end (A and 13), fit into a cast-iron stand, to which 
the enclosure is firmly bolted. 

when in the lathe (i.e.., in the plane in which any variation from the spherical shape 
would be a maximum) showed that the greatest divergence from the mean diameter 
did not exceed one hundredth of an inch. 

The cavity was cut out of a solid block of rolled steel through an opening only 
1|- inches diameter, a clever piece of engineering, for which I am indebted to 
Messrs. LEXNOX and Co. Exceptional care was also taken to give the inner walls a 
smooth polished surface. 

The internal volume of the cavity was redetermined by weighing the mercury 
required to fill it. From these determinations the diameter of the sphere is 10'20 
centims. The volume is, therefore, 556 cub. centims. and the internal surface 327 
sq. centims. 

The minimum thickness of the walls is 2|- inches, and the apparatus would doubtless 
withstand a pressure of 2000 atmospheres. As, however, the experiments had to be 
carried out in an ordinary laboratory, under conditions which would have rendered 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 367 

the consequences of an accident disastrous, it was decided not to exceed half this limit. 
The second enclosure was alone used for higher pressures, it being, as we shall see, of 
stronger construction. 

Apart from the effect of actual pressure, that of the sudden impact or blow given 
by the more rapid explosives has to be considered. As will be seen below, some 
mixtures of compressed coal gas and oxygen develop their full pressure in something 
like one ten-thousandth of a second and, in fact, occasionally detonate. It is difficult 
to estimate the actual strain produced by a force so suddenly applied.* When we 
consider that the present work comprised the repeated explosion of such mixtures, it 
will be seen that exact calculation becomes impossible. In all probability, during the 
course of the first few explosions of this kind the part of the material nearest the 
inner surface is strained to beyond its limit of elasticity, and therefore yields. In the 
case of steel, like the present, having a fair elongation, the first effect is actually to 
strengthen the enclosure ; the inner layers of the steel having been thus permanently 
elongated are under an initial compression which will help them in resisting further 
deformation. Aided, however, by the extremely rapid variations of temperature, this 
effect will in time cause surface cracks. Under successive strains the cracks will 
deepen to an extent that may become dangerous. Being on the inner surface of the 
chamber, the extent of the damage cannot be clearly ascertained. In the present 
work this danger was guarded against by a method which, though perhaps some- 
what crude, is at least easily carried out and, faute de mieux, may be considered 
satisfactory. On the outer surface of the enclosure a ring was accurately turned ; the 
plane through the centre of this ring passes through the centre of the sphere and 
through the gas and mercury inlets : it therefore encircles the weakest portion of the 
enclosure. A large micrometer gauge was made, by means of which the diameter of 
this ring was from time to time measured. This micrometer will clearly show an 
increase of one three-thousandth of an inch on the 8-inch diameter, or a change of 
about one two-hundredth of one per cent. 

Up to the present no variation of diameter has been detected, and it is reasonable 
to infer that the apparatus has not been strained to a dangerous extent. 

A sectional drawing of the enclosure is given in fig. 5. 

The recording gauge screws into A, the steel ring (D, fig. 3) pressing on to the 
ledge a and thus forming a joint. The end of the gauge fits closely into the neck 
b and protects the joint from contact with the heated gases. The firing plug fits 
into the aperture B. 

When gaseous mixtures are to be tested, the two valves which screw into C and D 
are brought into use. The cavity is first filled with mercury through C and the gas 
is then forced in through D. As soon as the mercury has been driven out, the valve 

* It is usual to take an instantaneous load as equivalent to twice the same statical load. In the present 
case, however, we have to deal with the momentum of the gas itself, which is travelling at an enormous 
speed. 



368 



ME. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 



C is closed and the pressure and composition of the mixture adjusted by means of the 
apparatus described below. 

After each explosion the sphere is washed out first with a solution of caustic 
potash, then with distilled water. 

Cylindrical Enclosure. 

The cylindrical enclosure, shown in fig. 6, is also made of mild steel. 

The dimensions are: external diameter 12 '2 centims. ; internal diameter 3 "17 
centims. ; length of bore 69'64 centims. It has, therefore, a capacity of 550 cub. 
centims. and an internal surface of 709 sq. centims. roughly speaking, the same 

D 




33" - 

Fig. 6. Cylindrical enclosure. 

The recording gauge screws in at A, the firing plug at B, and two valves at C and D respectively. The 
volume of this enclosure is nearly the same as that of the sphere, its surface 2 '17 times as great. 

volume as the sphere, but rather more than twice its surface. The various apertures 
are identical to those of the spherical enclosure and the gauges and other fittings can, 
therefore, serve for either apparatus. This cylinder has been used up to 2000 
atmospheres and would doubtless be safe at a considerably higher pressure. 

Firing Plug. 
The design of the firing plug is clearly shown in fig. 7. 

Standard Gauges. 

A vast number of measurements of statical pressure had to be made during the 
course of the work, more especially for the part dealing with gases. For this purpose 
the connections were arranged so that the gauges could be easily interchanged, each 
one being used for the range over which it was most sensitive. To determine the 
initial pressure and composition of the gaseous mixtures, two independent sets of 
observations were always taken. The pressure was first roughly adjusted to the 
desired amount by means of direct-reading Bourdon gauges, then accurately 
measured by a standard gauge. A series of mercury columns were used for the lower 
pressures and manometers of the Cailletet type for the higher pressures. The various 



EXPEEIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 



369 



small modifications introduced in the construction of the latter instrument, though 
they added to its reliability, are not of sufficient importance to warrant a more 
detailed description. 

Three gauges of this pattern were in use, the first reading from 3 to 12 atmospheres, 
the second from 12 to 50, the third from 50 to 200. 




EXPLOSION ENCLOSURE 



Fig. 7. Firing plug. 

The insulation of the central conductor is cone-shaped, to prevent its being forced out by the pressure of 
the explosion. A small cartridge of fine gunpowder can, when required, be placed round the fine 
wire W. The gas-tight cone joint D is protected, in the usual manner, from direct contact with the 
flame by a projecting piece, which closely fits the aperture in the explosion chamber. 



Valves and Connections. 

The various valves by which the flow of the gas is regulated are of the type shown 
in fig. 8. 

The gas inlet is at A, whereas B is connected to a gauge which indicates the 
pressures behind the valve. A fine screw-thread is cut on the spindle S. By turning 
the wheel W the conical end F of the spindle is lifted slightly from its seat and the gas 
flows to the part of the apparatus connected to C. To avoid any sudden rush of gas 
the spindle bears a slightly tapered prolongation, which nearly fits the outlet, and, 
therefore, several turns of the screw are necessary to give the full opening. 

The many connections required throughout the apparatus are all cone joints of the 
type shown at C. 

The female connection ends in a hollow cone, the angle being about 100 degrees. 
The male D is a cylinder of brass, an inch or two long, ending in a hemisphere, which 
is pressed into the cone by the nut N, the inner surface of which bears upon a ring K. 

VOL. ccv. A. 3 B 



370 



ME. J. E. PETAVEL ON THE PEESSUKE OF EXPLOSIONS. 

A 




Fig. 8. Valve and connecting cone. 

The numerous valves required during the present research were all substantially of the type shown in this 
figure, though varying considerably in external shape according to the use for which they were 
intended. The above design was used for the valves serving to regulate the initial pressure and 
composition of the mixture in the experiments on gaseous explosives. The apparatus is fixed firmly to 
the working bench by screws (not shown in figure) passing through the four corners of the metal block. 

Into this cylinder the copper tube is soldered for a distance of about three-quarters of 
an inch. These cone joints are superior to the lead washer joints, inasmuch as they are 
easily made or disconnected, last indefinitely, and remain gas-tight under all pressures. 

PART II. EXPERIMENTAL INVESTIGATION OF THE EXPLOSIVE PROPERTIES 

OF CORDITE.* 

The maximum pressure developed by explosives can be measured with considerable 
accuracy by means of the crusher gauge, which was devised some thirty-five years 
ago by Sir ANDREW NOBLE, t The classical work since carried out by this investigator 
is too well known to need a mention here. Attention may, however, be drawn to one 
of the more recent papers, in which NOBLE publishes the cooling curves of cordite 
and describes the instrument by which they were obtained.^ The apparatus is in 
principle not unlike an ordinary steam engine indicator, but the spring is initially 
compressed by an amount corresponding to nearly the full pressure of the explosion, 
and is automatically released when this pressure has been reached. By this ingenious 
contrivance the violent oscillations of the spring, which would be set up by the 
explosion itself, are avoided, and a clear record of the rate of fall of pressure is 
inscribed. 

* The explosive used in the course of this work was issued, by order of the Secretary of State for War, 
as representing the service cordite of the year 1902. Samples of three different sizes were included in the 
issue, the nominal sizes being 50/17, 20/17 and 3f. 

t 'Proc. Roy. Tnst.,' vol. VI., p. 282, 1871; see also 'Phil. Trans. Roy. Soc.,' vol. 165, p. 49, 1875, and 
'Phil. Trans.,' vol. 171, p. 203, 1880, &c. 

| 'Proc. Eoy. Inst.,' vol. 16, p. 329, 1900. 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 371 

In ballistic tests the total energy imparted to the projectile is calculated from the 
readings of the Holden-Boulanger chronograph, and, in the case of specially 
constructed experimental guns, the Noble chronograph gives valuable information on 
the distribution of pressure within the gun itself.* 

With regard to the more destructive explosives, such as blasting powders, 
dynamite, &c., their power is usually estimated by means of the Trauzlf lead block. 
At Woolwich this method has, however, been recently abandoned, an apparatus of 
the pendulum type being now in use.J 

By the above methods the maximum pressure and the rate of fell of the pressure, 
or at least the total energy, can in most cases be satisfactorily estimated. 

Comparatively little information is, however, available with regard to the initial 
part of the explosion; i.e., the behaviour of the explosive from the moment at which 
it is fired up to the time when it is fully consumed. 

This point deserves further investigation, the action of the explosive during this 
period being no less important than the question of the maximum pressure attained. 

It must be borne in mind that any structure, whatever its nature, will behave very 
differently according as it is exposed to a stress gradually applied, or is subjected 
suddenly to the same stress, or finally is submitted to violent oscillations of load. 

In the case of a gun any abnormally rapid explosion gives rise also to another 
source ot danger. The time elapsing between the ignition and the complete 
combustion of the charge may be insufficient to allow the inertia of the shot to be 
overcome and to move it through an appreciable distance. Should this occur, the 
products of combustion would be confined in an unduly small space, and the pressure 
would rise above the safe limit. 

The study of the initial stage of the explosion for various powders has formed part 
of the researches carried out by the Service des Poudres et Salpetres in Paris. The 
gauge first used by VIEILLE was a modification of the crusher gauge , while of late 
years he has worked with a new type of spring manometer. || 

In Germany, BICHEL, BRUNSWIG^ and others have suggested that the properties of 
explosives should be determined by measurements made at relatively low pressures, 
the results being deduced by extrapolation. Careful work has been carried out by 
BLOCHMANN** under these conditions. The gravimetric densities ft used are from O'Ol 

* 'Report Brit. Assoc.,' Oxford, 1894, pp. 523-540. 

t 'Ber. Int. Kong. Angew. Chem.,' Berlin, 1903, vol. II., pp. 299-303 and 462-465. 
I Captain DESBOROUGH'S report. See '25th Report of H.M. Inspector of Explosives.' 
'Comptes Rendus,' vol. 112, p. 1052, 1891. 

|| ' Memorial des Poudres et Salpetres,' vol. XL, pp. 157-210, 1902 ; see also ' Comptes Rendus,' vol. 115, 
p. 1268, 1892. 

H 'Ber. Int. Kong. Angew. Chemie,' vol. II., pj. 282-299, 1903. 
** 'DiNGLER's Poly. Journ.,' vol. 318, pp. 216 ar.d 332, 1903. 

tt Gravimetric density is defined as the ratio of the weight of the charge to the weight of that volume 
of water which would fill the enclosure ; it is, therefore, numerically equal to the specific gravity of the gas 
produced when the explosive is fired. 

3 B 2 



372 



MR. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 



to 0'02 and the maximum pressures recorded below one half ton per square inch. It 
is necessary to point out that such a method may not infrequently lead to most serious 
errors. 

Finally, it is generally understood that, in connection with this subject, numerous 
experiments have been carried out at Woolwich under the direction of Major HOLDEN, 
but no results have as yet been published. 

Experimental Work. 

A preliminary question to be decided, before starting the series of experiments, 
referred to the method of ignition. The usual practice is to fire the charge of cordite 
by means of a small quantity of fine powder, which is ignited either by a percussion 
cap, or by a metallic wire which is brought to incandescence by an electric current. 
Some records were taken in this way, but it was soon found that alterations in the 
amount and disposition of this firing charge, though leaving the actual maximum 
pressure almost unaffected, caused some variation in the shape of pressure curve (see 
fig. 9). When a relatively small quantity of the igniting charge is used in an 



o.oi 



0.0? 



0.03 




0.01 0.02 0.03 

Time in seconds. 



Fig. 9. Comparison of the effect of ignition by oxyhydrogen and gunpowder. 

Cordite of 0-175 inch diameter in a cylindrical enclosure; charge uniformly distributed; gravimetric 
density 1 ; A, fired with oxyhydrogen gas ; B, fired with fine-grained powder. 

enclosure of considerable length, only the part of the cordite in immediate proximity 
seems at first to take fire, and the flame is then propagated from layer to layer of the 
explosive. When the firing charge is larger, or the dimensions of the enclosure 



EXPEEIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 



373 



smaller, or, thirdly, when very fine cord is used, a more satisfactory ignition is 
obtained. This point in itself would be well worth more careful investigation, but as 
the present research refers principally to the properties inherent to cordite itself, it was 
desirable to be independent of such disturbing factors. The ideal conditions would be 
realised if a method could be found of igniting every particle of the explosive at the 
same instant over its entire surface. These conditions are approached by the process 
used. 

After the required quantity of cordite had been filled in and the explosion chamber 
closed, the air therein contained was displaced by a mixture of oxygen and hydrogen 
at, or near, atmospheric pressure, and this was fired off in the usual way by an electric 
current. The velocity of the explosion of this mixture is such that the effect of the 
gaseous combustion is practically over before the pressure of the burning cordite 
begins to make itself felt, and each cord, being entirely surrounded by the flaming 
gases, cannot fail to ignite over its entire surface. On the records the impact of this 
preliminary explosion is marked by a slight tremor occurring just before the actual 
rise of pressure occurs. The pressure due to the gaseous explosion is about 
10 atmospheres which, when compared with the 1000 or 2000 atmospheres resulting 
from the explosion of the cordite, does not form a serious correction. 

General Shape of the Curves. 

All the records exhibit certain general characteristics. The typical curve of rise of 
pressure is illustrated in fig. 1 0. It consists of three parts : (a) beginning nearly 



- Time in seconds. 
Fig. 10. Typical time pressure curve resulting from the explosion of cordite in closed vessel. 

asymptotical to the time axis and, gradually rising more rapidly, corresponds to the 
first stage of the combustion ; (b) referring to the full blast of the explosion, shows a 
much faster and almost constant rate of rise ; while at (c) the rapid decrease in the 
surface of the explosive can no longer be counterbalanced by the accelerating effect of 
the higher pressure. At c, therefore, the curve turns round sharply and merges into 
the cooling curve. So much for the general shape of the records. As we shall see 



374 



MR. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 



below, a more detailed study shows that, while conserving the same configuration, the 
actual curve may, according to circumstances, either be smooth (see Plate 21, figs. 1 
and 2), or made up of continuous vibrations (see Plate 21, fig. 3), or, thirdly, composed 
of a series of small but sharp steps corresponding with the successive impacts of the 
explosion wave (see Plate 21, fig. 4). 

Effect of the Diameter of Cordite. 

The velocity of the explosion depends primordially on the diameter of the cordite, 
but is modified to some extent by the distribution, the method of firing, and more 
especially by the gravimetric density. Fig. 1 1 shows the rise of pressure for three 



1 000 



o 

-^ 

a 
s 




0.01 0.02 



0.03 0.0* 0.05 0.06 
Time in seconds. 



0.07 0.08 0.09 



Fig. 11. Showing variation of rate of explosion with size of cordite used. 

Gravimetric density 1 ; charge uniformly distributed ; cylindrical enclosure used ; A, diameter of 
cord 0'035 inch; B, diameter of cord 0'175 inch; C, diameter of cord 0-475 inch. 

different diameters of cord (0'475 inch, 0'175 inch, 0'035 inch); the gravimetric 
density is in every case O'lO. The largest size is used for heavy ordnance, the smallest 
size for the army rifle. The three tests were made under the same conditions and in 
the same enclosure. 

Fig. 12 relates to a similar experiment carried out at a higher pressure. Lastly, in 
fig. 13, the time required for the complete combustion of cordite of various diameters 
is plotted for three distinct gravimetric densities. 

The relation between the time occupied by the explosion and the diameter of the 
cordite, as shown in this figure, is practically a linear one, the lines converging 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 



375 




0.02 



0.04 0.06 

Time in seconds. 



0.08 



Fig. 12. Showing variation of rate of explosion with size of cordite. 

Gravimetric density 0'15; charge uniformly distributed; cylindrical enclosure used; A, diameter 

of cord 0-175; B, diameter of cord 0-475. 



% 
1" 

A fl 




























01 5 o 

Diameter in millimetres. 










^ 


/ 


X 








^ 


^ 




iameter of cordite 

p < 

r\> la -I 








$ 


y^ 


'* 






^ 


^ 












/ 


// 


/& 


^ 


^ 


* 














,X 


r* 


^ 


^ 


















C^ 


<" 

























Q O.OI 0.0? 0.03 0.04 0.05 0.06 0.07 0.08 0.09 O.IO O.ll O.I2 

Time required to reach the maximum pressure (in seconds). 

Fig. 13. Effect of the gravimetric density and of the diameter of the explosive on the time required 

to reach the maximum pressure. 



376 ME. J. E. PETAVEL ON THE PKESSURE OF EXPLOSIONS. 

towards the zero of time and diameter. We may, therefore, conclude that the 
combustion of finely divided cordite is nearly instantaneous. Under such conditions 
the result of an explosion would be very destructive, and it is possible that some 
abnormal effects which have on certain occasions been observed may be due to the 
pulverisation of the explosive at any early stage of the combustion. 

However rapid an explosion may be, it remains, in principle, very distinct from a 
detonation. In an explosion the combustion is propagated from layer to layer without 
discontinuity. In a detonation the chemical reaction is practically instantaneous and 
simultaneous throughout the entire mass. The determining cause is, in this case, a 
compression wave of sufficient intensity to raise the material to its temperature of 
ignition. 

Let us take for the sake of illustration a numerical example, although the values 
employed can only be rough estimations, and suppose a sphere of cordite 1 centim. in 
diameter under a gravimetric density of O'l. If this were ignited in the ordinary 
way, the combustion would travel towards the centre of the sphere at an average rate 
of 8 centims. per second and the maximum pressure would therefore be reached in 
0'063 second. If, on the other hand, the material were to detonate, the detonation 
wave would travel through the mass at a speed of something like 800,000 centims. 
per second,* and the total time occupied would be one hundred thousand times 
less. 

In an explosion we have usually to deal with pressures which may be considered as 
statical as far as their action is concerned ; in a detonation with a dynamical pressure 
or impact. The impact of the products of combustion travelling with enormous 
velocity may correspond in effect to an instantaneous pressure five or ten times 
greater than the normal pressure calculated from the composition of the explosive and 
its heat of reaction. 

A typical case of this kind occurred when working with a compressed mixture of 
coal gas and oxygen. The total pressure of the explosion should have been some 4 or 
5 tons per square inch. The mixture, however, detonated, and the solid steel piston 
of the recorder, though encased in a steel cylinder over 2 inches thick, was expanded 
outwards like the head of a rivet, t It is not easy to estimate exactly the statical 
pressure required to produce a corresponding effect, but it cannot be less than 25 tons 
per square inch. 

To return now to the work on cordite, the results obtained with one of the smallest 
diameters in use are shown in fig. 14. It will be seen that, though the time occupied by 
the combustion is small, amounting to less than O'OOS of a second, the shape of the 

* ABLE found that the rate of detonation of a train of dynamite or guncotton was about 608,000 
centims. per second. See also SEBERT, BERTHELOT and METTEGANG. The latter (' Ber. 5. Int. Kong. Ang. 
Chem., Berlin, 1903,' vol. II., p. 322) gives 700,000 centims. per second as the detonation rate of dynamite. 

t A similar effect is recorded hy NOBLE ('Proc. R. I.,' 1900), as having been produced on the copper of 
a crusher gauge by a charge of lyddite. 



EXPEEIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 



377 



curve is perfectly normal, showing clearly the three distinct stages of combustion 
referred to on p. 373. 

The law of combustion by parallel surfaces as expounded by VIEILLE* applies well 
to the case of cordite, t 



0.005 



0.010 



0.015 




0.005 



0.010 

Time in seconds. 



0.015 



Fig. 14. Showing the rate of rise of pressure for cordite of the smallest diameter. 
Diameter 0'035 inch (0'89 millim.). 

A, spherical enclosure ; charge uniformly distributed ; gravimetric density 074. B, cylindrical enclosure ; 
charge uniformly distributed ; gravimetric density 0'075. C, cylindrical enclosure; charge concen- 
trated in one quarter of cylinder, nearest the recorder; gravimetric density 0'075. 

The speed at which the flame travels inwards towards the centre of each cord is 
uniform and relatively slow. When unconfined, cordite burns at a rate of about 
0'5 centim. per second. In a closed vessel the average speed increases to 5 centims. 
per second for an explosion developing 500 atmospheres, 8 centims. for a maximum of 
1000 atmospheres, and 11 centims. per second for 2000 atmospheres.^ 

The shape of the curve representing the rise of pressure depends essentially on two 

* 'Comptes Eendus,' vol. 118, pp. 346, 458, 912; 1894. 

t The peculiarly regular combustion of cordite was first noticed by NOBLE, who in 1892 ('Proc. Roy. 
Soc.,' vol. 52, p. 129) remarks that the pieces of cordite blown from the muzzle of the experimental gun he 
was using were so uniformly decreased in diameter that they might readily have been mistaken for newly 
manufactured cordite of smaller diameter. 

| The time required for the full pressure to develop is, therefore, proportional to the diameter of the 
cord. The formula L == r/c (where L is the time in seconds and the radius in centimetres) gives a fair 
approximation, though, as we shall see, the actual time varies somewhat, according to the conditions of the 
experiment. The constant c is characteristic of the explosive and, of course, equal to the above rates of 
combustion. 

VOL. CCV. A. 3 C 



378 ME. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 

factors : (1) on the surface of the explosive exposed to combustion and hence on the 
radius of the cords at each instant during the reaction ; (2) on the radial speed at which 
the zone of combustion is travelling towards the centre of each cord. This speed may 
be taken as proportional to the pressure. The formula S = ap (where S is the speed 
in centimetres per second, p the instantaneous pressure in tons per square inch, and a 
an empirical constant equal to about 3 '5) may be of use where it is not possible to make 
a direct experimental determination. 

The maximum pressure (P) developed by a given charge is usually well known, and 
by aid of the above formula the curve of rise of pressure can therefore be obtained 
The radius of the cordite for successive intervals of pressure (p = O'l P, p = 0'2P, 
&c.) is first computed, and the time required to burn through the corresponding 
distance at the average pressure (p = 0'5 P, p = 0'15 P, &c.) is then determined. In 
calculating the radius, the volume of the unburnt explosive must, of course, be taken 
into account, and this renders the work somewhat tedious. 

The formula does not take into account the fact that under experimental conditions 
some time elapses while the flame is spreading before the normal rate of combustion is 
set up. The zero of the calculated curve is, therefore, shifted somewhat to the right, 
and a sharper slope given to the initial stage (a, fig. 10). 

It may with some truth be argued that the error occurring at a very low pressure 
would not affect the results as applied to ballistics, the calculation arid experimental 
curves being in agreement by the time the motion of the shot commences. It is 
hoped, however, that the day is not far distant when we shall be able to obtain an 
indicator card from a gun with the same ease as we now indicate other heat engines ; 
approximate calculations such as the above will then cease to be of practical value. 

We have explained above the system used for firing the charge. When the key 
is pressed, the atmosphere of oxyhydrogen, with which the enclosure has been filled, 
explodes and the cordite is surrounded by a sheet of flame. The time at which this 
takes place is recorded by a slight tremor of the gauge. The charge does not ignite at 
once,* for though the explosive is surrounded by an intensely hot flame, a quite 
appreciable time is required for its surface to rise to the temperature of ignition, t 

The ignition begins at the ends of each stick or at other parts, where, for instance 
owing to a blister, the conductivity has been reduced. The last parts to be attacked 
are those which were in contact with the walls of the enclosure or with some other 
portion of the charge. These circumstances, together with a slow rate of combustion 
which is characteristic of cordite under very low pressures, account for the gentle 
slope of the first part of each curve. 

* In the appended tables and curves, time is counted from the instant the cordite ignites, as marked by 
the first permanent rise of pressure. 

t A stick of cordite may under ordinary conditions be passed comparatively slowly through the flame 
of a Bunsen burner without igniting. If, however, its surface has previously been scratched or scored, the 
smaller particles will ignite at once and set fire to the mass. 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 379 

When fully ignited, each particle is freely suspended in space, being kept from direct 
contact with other bodies by the rush of flame issuing from its surface. It is to 
these conditions that the law of combustion by parallel layers accurately applies. 

While the combustion is taking place, heat is being continually transmitted to the 
walls of the enclosure, and the maximum pressure attained will therefore be less for a 
slow explosion than for a fast one ; the actual effect may be seen by reference to 
figs. 11, 12 and 15. 

The heat loss accounts also, as stated above, for the manner in which the curves of 
rise and fall of pressure merge together. By the time the maximum pressure is nearly 
reached the diameter of each particle of explosive is greatly reduced. The weight of 
substance consumed per unit time begins therefore to decrease, although the flame is 
actually advancing towards the axis of each cord at an ever increasing speed. Finally, 
the combustion just counterbalances the total thermal loss, and the curve of pressure 
remains for an instant practically constant at its maximum value. This will be seen 
clearly in figs. 1 and 2 on Plate 21. 

Effect of the Enclosure. 

We have just referred to the thermal loss due to the cold walls of the explosion 
chamber. The total loss, cceteris paribus, is proportional to the time. 

When the diameter of the cordite, and consequently the time occupied by the 
combustion, is very small, the theoretical value of the maximum pressure is closely 
approached, and the shape and size of the enclosure have but little effect (compare 
A and B, fig. 14). These factors become, however, of considerable importance in 
determining the maximum pressure developed by the slower burning cordite (see 
fig. 15). 

The shape of the cooling curve depends, on the other hand, essentially on the 
dimensions of the enclosure. In fig. 16 the facts are clearly illustrated by the results 
of comparative experiments carried out respectively in a sphere and in the cylinder. 

It is proposed to reserve the general discussion of the questions of dissociation and 
rate of cooling for the third part of the present research ; we shall then be dealing 
with gaseous mixtures of simple composition which will serve as a natural introduction 
to the consideration of more complicated questions. A few words are, however, 
necessary with regard to the somewhat unusual conditions under which the cooling 
of the products of combustion of a solid explosive takes place. 

Under ordinary circumstances the convection and conductivity of the gas itself are 
the ruling factors which determine the rate of cooling. 

The thermal capacity of the gaseous mixture and the rate at which heat can be 
transmitted through it are low compared with the corresponding properties of the 
enclosure. These facts hold true whether the latter is water-cooled or not. 

In such cases neither the inner surface of the enclosure nor the layer of gas in 

3 c 2 



380 



ME. J. E. PETAVEL ON THE PKESSUKE OF EXPLOSIONS. 




0.4 0.6 

Time in seconds. 



0.8 



1.0 



Fig. 15. Showing the effect of the shape of the enclosure on the maximum pressure developed 

by cordite of large diameter. 

Gravimetric density 1 ; charge uniformly distributed ; A and AI, in spherical enclosure ; B and BI, in 
cylindrical enclosure; A and B, diameter of cord 0'475 inch (12 '07 millims.); AI and BI, diameter 
of cord 0-175 inch (4 -44 millims.). 

contact with it rise much above atmospheric temperature, and the rate at which heat 
is dissipated depends on the temperature gradient which is set up in the gaseous 
mass. 

In previous papers* I have pointed out how the rate of transmission of heat in a 
gas varies with the pressure. In the case of air, for instance, the law 

E x 10 6 = 403p' M + 1 -63/' 21 3 

was verified up to 1000 C. and 170 atmospheres, t At this pressure already air 
transmits heat at the same rate as a substance having twenty times the conductivity 
of air at atmospheric pressure. 

* 'Phil. Trans.,' A, vol. 191, pp. 501, 524, 1898; and vol. 197, pp. 229-254, 1901. 

t E is the heat abstracted from each square centimetre of surface of the hot body measured in therms 
per second per degree temperature interval. 5 is the temperature of the hot surface measured in degrees 
Centigrade, and p the pressure of the surrounding gas in atmospheres. 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 



381 




0.2 



0.3 0.4 0.5 

Time in seconds. 



0.6 



0.7 



0.8 



Fig. 16. Effect of the dimensions of the enclosure on the rate of cooling of the products of 

combustion. 

A, cylindrical explosion vessel; gravimetric density 0-15; diameter 0-175; uniformly distributed. 



B, 

C, spherical 

D, 

E, cylindrical 

F, " 
G, 

H, ,, 



0-15: 

0-1 ; 

0-1 ; 

0-1 ; 

0-1 j 

0-1 : 

0-1 : 

0-1 ; 



0-475; 

0-175; 

0-475; 

0-035; 

0-175; 

0'175; not uniformly distributed. 

475 ; uniformly distributed. 

" 475 ; not uniformly distributed. 



When considering the products of an explosion, it must be remembered that the 
effective conductivity of the gas is further increased by its state of rapid motion. It 
is also augmented by the large proportion of hydrogen and water vapour contained 
therein. 

As a result the temperature of the walls of the enclosure rises rapidly as the cooling 
of the gas proceeds, and before long the rate of cooling will depend essentially on the 
conductivity of the walls of the enclosure and not on the properties of the gas. The 
heat abstracted per unit time will then be simply proportional to the temperature. 

If the logarithmic decrement of the latter part of the curve is measured, it will be 
found that the theory is confirmed in this respect by the results of the experiments. 



382 ME. J. E. PETAVEL ON THE PEESSURE OF EXPLOSIONS. 

The quantity of heat which is transmitted to the walls of the enclosure during the 
brief period occupied by the cooling of the gas is much greater than would occur in 
cases met with in ordinary engineering practice. With a gravimetric density of O'l 
the amount of heat to be absorbed per unit surface of our cylindrical enclosure is some 
hundred times as large as that which would be absorbed by the cylinder of an ordinary 

gas engine. 

In the case of artillery of large calibre the inner surface of the steel probably 
attains a temperature close to its melting-point and the correspondingly plastic 
material yields easily under the combined friction and chemical action of any escaping 
gas. In the case of small arms, the temperature being limited by the relatively small 
volume and therefore small thermal capacity of the gaseous mass, practically no 
erosion takes place. 

To return now to the experimental work. In the following table the time required 
for the pressure to fall to three quarters, one half, one quarter of its maximum value 
is given for a number of distinct experiments, whereas the cooling curves for three 
different diameters of cordite at gravimetric densities of O'l and O'l 5 will be found 
plotted in fig. 16. It is noticeable that after the first tenth of a second the curves 
taken under similar conditions, but for various sizes of explosive, lie closely together, 
showm' r that the diameter has no material effect on the subsequent rate of cooling. 

When we refer, however, to the table, we see that the times required to reach a 
given fraction of the maximum are different for different diameters. 

This apparent discrepancy is explained by the fact that the total quantity of heat 
absorbed is primordially a function of time. When the combustion is very rapid, the 
maximum pressure is reached while the walls of the enclosure are still cold and the 
percentage fall of pressure per unit time is high. With a slow-burning cordite the 
surface of the enclosure becomes considerably heated during the combustion of the 
explosive, and after the maximum the percentage fall of pressure is correspondingly 
lower. Briefly stated, at any fixed interval of time after ignition the total heat 
absorbed by the enclosure, and, therefore, the temperature of its inner surface, will be 
nearly the same for all diameters of the explosive. In consequence, the rate of cooling 
as measured by the rate of change of pressure at any stated time is unaffected by 
the speed of combustion. 

The rate of cooling for a given volume of the enclosure does not vary, as is usually 
assumed, in proportion to the surface, but nearly as the square of the surface. 

It will be noticed that the cooling in the cylinder is about four times as rapid as in 
the sphere, whereas the ratio of the two surfaces is as 2 '17 to 1. 

In such massive enclosures the heat generated by the explosion is at first entirely 
absorbed by the inner layers of the steel walls. It does not travel to the outside 
until some time after the explosion is over, A decrease in the surface has, therefore, 
a double effect. The heat to be absorbed per unit area and the average thickness of 
metal through which this heat must be transmitted are both increased. 






EXPEKIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 



383 



a 



o 
O 

o 

03 



'S 



.9 

^-H 

o 

6 

C*H 

o 

H 
EH 

1 

PH 





>b 








t-O 




00 




I 1 r 1 




ic (M 




O O 




O 




io 








t- O 


e 


O OJ t~ 




p I t 




r-H <M t~ 






o 









F* 


O 




^ 


'c 






ib 


tS 






t~ 


a 


C-l CO 




-* r-H 


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r-H CO 




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o o 




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^> r H ^ 




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o o o 




io 10 








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73 


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t- IO 


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p 


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t- 10 




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fe 


r f, CO o 




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o o o 




t- o 


p '} 


CO IO CM 




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p 


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o o o 




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l-H r-H 




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^oiS ocsocS 


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o & 





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g^Sceg^csS-SPs 




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384 



ME. J. E. PETAVEL ON THE PKESSURE OP EXPLOSIONS. 



Relation of Pressure to Gravimetric Density. 



The present work was not taken up with a view to specially investigating the above 
subject, which has already been fully treated by NOBLE. It is, however, of interest 
to compare the results with the much more complete set published by this 
investigator. 

To minimise the effect of the rapid rate of cooling, which, as we have just seen, is 
inherent to small enclosures, we must select for comparison the values obtained when 
using cordite of relatively small diameter. The pressures obtained with cordite of 
0'175 inch and - 035 inch diameter are shown in fig. 17, marked in on the curve 
representing NOBLE'S results, and are, as will be seen, in close agreement with it. 




OJ5 



Gravimetric density. 
Fig. 17. Variation of maximum pressure with the gravimetric density of the charge. 

The curve is traced out from the values given by Sir ANDREW NOBLE ; the points marked on it refer 
to the results incidentally obtained in the course of the present work. 

Though the pressure and temperature are exceptionally high, there is no reason for 
supposing that the products of combustion depart considerably from the law which 
governs the pressure of gases at ordinary temperatures. 

This law may be written 



In the present case, where the temperature is very high and constant, we may put 
RT = c, and for a first approximation neglect cohesion of the gas. 
The formula then takes the simple form 

p (vb) = c. 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 



385 



The volume to which the gas will be reduced under infinite pressure may be taken 
as closely approaching the inverse of the density of the solid explosive. Therefore 



b = 



1-56 



= 0-641, 



whereas v is the inverse of the gravimetric density p. 
Thus 

c = -0'641. 
P 

To minimise the error due to cooling we will take the value of p obtained for the 
smallest cordite in the spherical enclosure. At a gravimetric density of 0'0744 this 
is 5'137 tons per square inch (see Table VI.), and therefore 



c _ 



0-0744 
The pressure developed by the explosive is 



o-641 x 5-137 = 6575. 



P = 



cp 

" " 



-bp " 1-0-64 l 



The results calculated from this formula are compared in the following table with 
NOBLE'S values and with those obtained during the course of the present work* : 







Pressure determined 


Pressi 


Gravimetric density. 


Pressure calculated. 


experimentally by 


expo 






NOBLE. 




0-05 


3-40 


3-00 




0-10 


7-03 


7-10 




0-15 


10-91 


11-30 




0-20 


15-08 


16-00 




0-30 


24-42 


26-00 




0-40 


35-37 


36-53 




0-50 


48-38 


48-66 




0-60 


64-10 


63 33 





nitally by 
PKTAVEI.. 



2-87 

7-01 

11-48 



In the above table the pressures are expressed in tons per square inch. 

The experimental results are influenced by many factors, such as the size of the 
enclosure, the dimensions of the explosive, and the oscillations of pressure, which are 
doubtless occasionally .set up. On the other hand, the formula we have used does not 

* When the pressure is measured in kilogrammes per square centimetre the constant c becomes 10355, 
whereas t. = 10021 gives the pressure in atmospheres, the constant b in either case remaining unaltered. 
A formula similar to the above was used by NOBLE and ABEL in connection with their researches on fired 
gunpowder. They assumed that the gases strictly followed BOYLE'S law, but introduced a factor (1 -- a.p) 
to allow for the space occupied by the solid residues left after the explosion. 

VOL. COV. A. 3 D 



386 



MR. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 



take into account the cohesion of the gas, or allow for the possible variation of the 
value b with temperature and density. 

Taking these circumstances into account, the agreement between the theoretical 
and experimental values may be considered satisfactory. 

Distribution of the Explosive. 

In a long narrow vessel a certain amount of vibration almost invariably occurs 
during the combustion of the explosives. If the explosive is concentrated in one part 
only of the enclosure, the effect is increased and the pressure rises by sharp steps, as 
shown in fig. 18. With some powders the sudden increments of pressure become 




T~/ME v 

Fig. 18. Diagram showing the type of vibration set up at the commencement of an explosion when the 
charge placed in a long enclosure is not uniformly distributed. The successive sharp increments of 
pressure correspond with successive impacts of the wave. 

dangerously large and an abnormally high maximum is reached in one or two steps. 
This phenomenon seems to be the transition between an explosion and a detonation. 

That it is difficult, in fact almost impossible, to detonate cordite has long been 
recognised as one of its principal advantages. Nevertheless, signs of abnormal 
explosion were visible whenever the charge was crowded together in one part of the 
enclosure. A fairly typical case is shown in fig. 4, Plate 21, a similar effect being 
recorded in many other cases, notably F 68, F 69, and F 70 (Tables XL, XII., XIII.). 

The experiments in this direction had to be confined to pressures of about 
1000 atmospheres. From these tests it seems probable that by working under similar 
conditions, but with a higher gravimetric density, cordite would give results not 
unlike those obtained by VIEILLE* in the case of " B.F." and other powders. 

* See "Etude des Pressions Ondulatoires," 'Annales des Poudres et Salpetres,' vol. III., pp. 177-236. 
VIEILLE, in the course of this work, obtained instantaneous pressures amounting to three times the normal 
value. Using a method of calculation similar to that given below, he showed that the speed of propagation 
of the smaller disturbance is in fair agreement with the speed of sound in the same medium. 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 387 

Unfortunately, for this very reason, the experiments could not be carried out in a 
laboratory. 

The sharp steps which go to make up these records may be accounted for in the 
following manner : When the explosive, which is packed closely at one end of the 
chamber, bursts into flame, a pressure wave is sent out which travels to the end of the 
cylinder and is then reflected back. When this wave, on its return journey, reaches 
the explosive, the combustion, which in the meantime had been proceeding uniformly, 
is accelerated in proportion to the increased pressure. The case is one of rmitual 
reaction between the two phenomena. Any irregularity in the combustion tends to 
start a pressure wave which in turn enhances this irregularity. The process is 
cumulative in its effects, and with the high gravimetric densities used in ballistic 
work it may, and doubtless occasionally does, cause disastrous results.* 

Incidentally the present work confirms ViEiLLE'st views as to the discontinuity of 
pressure set up by wave actions, the successive steps of the curve rising abruptly, if 
not instantaneously. 

The velocity of propagation of the wave is measured directly by the time elapsing 
between the successive sharp increments of pressure which are recorded. 

When a wave is set up at the commencement of the explosion, the impacts on the 
recording gauge succeed each other at intervals of 0'00125 or 0'00121 second when 
the charge in the cylinder is at gravimetric densities of O'lO or 0*15 respectively. 
The path traversed, i.e., the double length of the enclosure, is 139'3 centime, and the 
corresponding velocities 1114, 1150 metres per second. \ 

Occasionally, when cordite of the smallest diameter is used, the wave motion is still 
sharply defined at the maximum pressure. The time interval is then O'OOHO second 
for a gravimetric density of 0*1 and the speed 1266 metres per second. 

From the general formula for the velocity of sound we can calculate the theoretical 
speed under these circumstances, 



V= A/ 
P 

These factors, with the exception of y, are well known, 

When the combustion is complete, the density, p, of the resulting gases is equal to 
the gravimetric density of the charge. 

The elasticity, E, is measured by the rate of change of pressure with density. 



* See CORNISH, 'Proc. Inst. Civ. Eng.,' vol. 144, p. 241, 1901. 
t 'Memorial des Poudres et Salpetres,' vol. 10, pp. 177-260, 1899-1900. 

| Theoretically the speed should be the same in either case ; the thermal loss, which is relatively less 
at higher gravimetric densities, probably accounts for the difference. 

3 D 2 



388 MR. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 

It can, therefore, be obtained by differentiating the expression 



which was given on p. 385. 

Carrying out this operation we find 



The value of the ratio of the specific heats, y, is somewhat uncertain. For the 
mixture of gases resulting from the explosion, y may be taken as 1'35 or 
P21, according as the specific heats are considered constant or variable with 
temperature. 

The following table gives the velocity of sound, calculated according to each of the 
above hypotheses : 

VELOCITY of Sound in the Gases Produced by the Combustion of Cordite at the 
Maximum Pressure of the Explosion, measured in Metres per Second. 



Gravimetric density. 


Velocity for = 1 35. 


Velocity for = 1-21. 


o-i 


1251 


1185 


0-2 


1343 


1272 


0-3 


1450 


1373 


0-4 


1575 


1491 


0-5 


1723 


1632 


0-6 


1903 


1801 



The limiting value for low densities, which should correspond with the speed of the 
wave at the commencement of the explosion, works out at 1170 (y = 1'35) or 1108 



Although, strictly speaking, the above theory applies only to very small disturb- 
ances, the calculated velocities are in fair agreement with the measurements given on 
p. 387. 

The oscillations referred to in the preceding paragraph are superimposed on the 
curve of pressure without directly altering its general shape. Within the limits of 
the present experiments the wave action, consequent on the uneven distribution of 
the charge, by increasing the thermal loss slightly lowers the maximum pressure. 
The rate of combustion is, also, somewhat altered ; usually it is accelerated. 

These effects will be best understood by reference to figs. 14, 19, and 20, in which 
the mean values of the pressure are plotted in terms of the time. 



1000 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 

0-01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 



389 




o.oa 



0.03 0.04 0.05 

Time in seconds. 



0.06 



0.07 



0.08 



jLime in suconus. 

Fig. 19. Variation of the rate of combustion and of the maximum pressure produced by a non- 
uniform distribution of the charge. 

Cylindrical enclosure; gravimetric density O'l ; diameter of cord 0'475 inch (12 "07 millims.). A, charge 
uniformly distributed ; B, charge placed in one sixth of the cylinder near the recorder. 



0.005 



O.oio 



0.015 



o.oeo 



O.OiO 



0.035 




0.005 



0.010 



0030 



0.035 



0.015 o.oeo o.oas 

Time in seconds. 

Fig. 20. Variation of the rate of combustion and of the maximum pressure produced by a non- 
uniform distribution of the charge. 

Cylindrical enclosure; gravimetric density - 1 ; diameter of cord 0-175 inch (4'44 millims.). A, charge 
uniformly distributed; B, charge placed in one half of the cylinder farthest from the recorder; 
C, charge placed in one sixth of the cylinder farthest from the recorder. This case is somewhat 
exceptional. The charge was so closely packed that it formed a nearly solid mass, which was probably 
scattered on ignition by the pressure of the gas produced behind it. 



390 



MR. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 



Generally speaking, the results obtained confirm the remarkable properties ot 
cordite with regard to its high power and to the regularity of the effects produced. 
It would doubtless be very desirable to extend the research to higher pressures and 
carry out, on similar lines, a comparative study of other explosives. Treated, however, 
in this general way the subject is too vast to be dealt with single-handed, and the 
writer can but express a hope that others more competent and better equipped will be 
found willing to take up the work. 

Before closing I desire to thank Professor ARTHUR SCHUSTER for placing at my 
disposal the ample resources of his laboratory. 

The cost of the apparatus has to a large extent been defrayed by funds awarded by 
the Government Grant Committee of the Royal Society, while for the cordite I am 
indebted to the courtesy of the War Office authorities. 



APPENDIX. 

In the following tables numerical results obtained from the measurements of the 
principal photographic records will be found. 

Where wave action is set up, the pressure given is the mean value of the 
instantaneous pressure at the time indicated. 



TABLE I. (Record No. F 55.) 

Spherical explosion vessel ; charge uniformly distributed ; gravimetric density - 0496 ; diameter of cord 

0-475 inch (12-07 millims.). 

Maximum pressure 404 atmospheres (2 '65 tons per square inch); time required to reach 
the maximum pressure 0'120 second. 



Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


o-oio 


10 


0-130 


404 


0-020 


22 


0-200 


397 


0-030 


31 






0-040 


43 






0-050 


67 






0-060 


98 






0-070 


150 






0-080 


215 






0-090 


287 






0-100 


363 






0-110 


397 






0-120 


404 







EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 



391 



TABLE II. (Record No. F 56.) 

Spherical explosion vessel ; charge uniformly distributed ; gravimetric density 0496 ; diameter of cord 

0-175 inch (4-44 millims.). 

Maximum pressure 438 atmospheres (2-87 tons per square inch); time required to reach 
the maximum pressure 045 second. 



Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


0-005 


24 


o-ioo 


438 


o-oio 


48 


0-200 


421 


0-015 


86 


0-300 


390 


0-020 


131 


0-400 


364 


0-025 


187 


0-500 


339 


0-030 


271 






0-035 


383 






0-040 


433 






0-045 


438 






0-050 


438 


i 



TABLE III. (Record No. F 57.) 

Spherical explosion vessel; charge uniformly distributed; gravimetric density 0'024; diameter of cord 

0-035 inch (0-89 millim.). 

Maximum pressure 144 atmospheres (0-95 ton per square inch) ; time required to reach 
the maximum pressure 0-014 second. 



Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


0-002 


12 


0-020 


144 


0-004 


28 


0-050 


143 


0-006 


52 


0-100 


141 


0-008 


77 






0-010 


103 






0-012 


127 






0-014 


144 







392 



MR. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 



TABLE IV. (Eecord No. F 59.) 

Spherical explosion vessel; charge uniformly distributed; gravimetric density 0-099; diameter of 

0-475 inch (12-07 millims.). 

Maximum pressure 1069 atmospheres (7-01 tons per square inch); time required to reach 
the maximum pressure 065 second. 



cord 






Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


0-005 


10 


0-070 


1069 


o-oio 


34 


o-ioo 


1062 


0-015 


53 


0-200 


993 


0-020 


79 


0-300 


935 


0-025 


113 


0-400 


883 


0-030 


160 


0-500 


840 


0-035 


244 


0-600 


804 


0-040 


357 


0-700 


773 


0-045 


521 


0-800 


746 


0-050 


684 


0-900 


716 


0-055 


880 


1-000 


689 


0-060 


1024 






0-065 


1069 







TABLE V. (Record No. F 60.) 

Spherical explosion vessel; charge uniformly distributed; gravimetric density 0-099; diameter of cord 

0-175 inch (4-44 millims.). 

Maximum pressure 1115 atmospheres (7 -31 tons per square inch); time required to reach 
the maximum pressure 0-022 second. 









Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


0-002 


29 


0-024 


1112 


0-004 


59 


0-030 


1109 


0-006 


103 


0-100 


1062 


0-008 


150 


0-200 


986 


0-010 


229 


0-300 


927 


0-012 


370 


0-400 


874 


0-014 


522 


0-500 


821 


0-016 


754 






0-018 


971 






0-020 


1089 






0-022 


1115 







EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 



393 



TABLE VI (Record No. F 61.) 

Spherical explosion vessel; charge uniformly distributed; gravimetric density 0-0744; diameter of cord 

0-035 inch (0-89 millim.). 

Maximum pressure 783 atmospheres (5-137 tons per square inch); time required to reach 
the maximum pressure 0-008 second. 



Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


o-ooi 


23 


o-oio 


783 


0-002 


85 


0-015 


783 


0-003 


202 


0-020 


772 


0-004 


381 


0-050 


769 


0-005 


616 


o-ioo 


728 


0-006 


763 


0-200 


669 


0-007 


774 


0-300 


622 


0-008 


783 


0-400 


587 











TABLE VII. (Record No. F 63.) 

Cylindrical explosion vessel; charge uniformly distributed; gravimetric density 0-1004; diameter of cord 

0-475 inch (12-07 millims.). ; temperature 18-6 C. 

Maximum pressure 916 atmospheres (6-01 tons per square inch); time required to reach 
the maximum pressure 070 second. 



Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


o-oio 


76 


0-075 


916 


0-020 


139 


0-080 


916 


0-030 


231 


0-090 


892 


0-040 


400 


o-ioo 


866 


0-050 


618 


0-200 


694 


0-060 


843 


0-300 


562 


0-065 


909 


0-400 


463 


0-070 


916 


0-500 


397 






0-600 


331 






0-700 


291 






0-800 


255 






0-900 


225 






1-000 


198 



VOL. CCV. A 



3 E 



394 



MR. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 



TABLE VIII. (Kecord No. F 65.) 

Cylindrical explosion vessel; charge uniformly distributed; gravimetric density 0-1004; diameter of cord 

0-175 inch (4-44 millims.). ; temperature 18 C. 

Maximum pressure 1041 atmospheres (6-83 tons per square inch); time required to reach 
the maximum pressure 0-028 second. 



Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


0-005 


66 


0-030 


1031 


o-oio 


192 


0-035 


1005 


0-015 


298 


0-040 


992 


0-020 


579 


0-050 


959 


0-025 


959 


0-060 


936 


0-028 


1041 


0-070 


909 






0-080 


879 






0-090 


860 






0-100 


826 






0-200 


645 






0-300 


512 






0-400 


423 






0-500 


347 






0-600 


298 






0-700 


265 






0-800 


235 



TABLE IX. (Record No. F 66.) 

Cylindrical explosion vessel; charge uniformly distributed; gravimetric density 0-0753; diameter of cord 

0-035 inch (0'89 millim.) ; temperature 19 '0' C. 

Maximum pressure 793 atmospheres (5-20 tons per square inch); time required to reach 
the maximum pressure 007 second. 



Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


0-001 


26 


0-008 


787 


0-002 


102 


0-009 


783 


0-003 


195 


o-oio 


777 


0-004 


324 


0-015 


760 


0-005 


453 


0-020 


750 


0-006 


658 


0-025 


721 


0-007 


793 


0-030 


701 






0-050 


655 






o-ioo 


539 






0-150 


456 






0-200 


380 






0-300 


281 






0-400 


212 






0-500 


179 






0-600 


152 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 



395 



TABLE X. (Record No. F 67.) 

Cylindrical explosion vessel ; charge all in half of cylinder farthest from the recorder ; gravimetric density 
0-1004 ; diameter of cord 0-175 inch (4 -44 millims.) ; temperature 19 C. 

Maximum pressure 1035 atmospheres (6 -79 tons per square inch) ; time required to reach 

the maximum pressure 026 second. 



Time in seconds. 


Pressure in atmospheres. 


0-002 


33 


0-004 


66 


0-006 


93 


0-008 


152 


o-oio 


188 


0-012 248 


0-014 


317 


0-016 


430 


0-018 


549 


0-020 


694 


0-022 


833 


0-024 


955 


0-026 


1035 



Time in seconds. 


Pressure in atmospheres. 


0-028 


1031 


0-030 


1025 


0-032 


1018 


0-034 


1015 


0-040 


992 


0-050 


959 


0-060 


925 


o-ioo 


826 


0-200 


654 


300 


529 


0-400 


456 


500 


387 


0-600 


340 


0-700 


298 


0-800 


258 


0-900 


222 



TABLE XL (Record No. F 68.) 

Cylindrical explosion vessel ; charge all in one-sixth of cylinder farthest from the recorder ; gravimetric 
density 1-004; diameter of cord 0-175 inch (4-44 millims.); temperature 18'6 C. 

Maximum pressure 1002 atmospheres (6'57 tons per square inch) ; time required to reach 
the maximum pressure 0-030 second. 



Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


0-002 


33 


0-032 


1002 


0-004 


60 


0-034 


995 


0-006 


86 


0-040 


985 


0-008 


106 


0-050 


942 


o-oio 


149 


0-060 


919 


0-012 


179 


0-100 


820 


0-014 


241 


0-200 


621 


0-016 


307 


0-300 


522 


0-018 


387 


0-400 


423 


0-020 


509 


0-500 


337 


0-022 


648 


0-600 


281 


0-024 


777 






0-026 


879 






0-028 


975 






0-030 


1002 







3 E 2 



396 



MR. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 



TABLE XII. (Record No. F 69.) 

Cylindrical explosion vessel ; charge all in one-sixth of cylinder near the recorder ; gravimetric density 
0-1004 : diameter of cord 0-475 inch (12-07 millims.) ; temperature 18 C. 

Maximum pressure 906 atmospheres (5 94 tons per square inch) ; time required to reach 
the maximum pressure 70 second. 



Time in seconds. 


Pressure in atmospheres. 


Time in second 


o-oio 


43 


0-075 


0-015 


73 


0-080 


0-020 


106 


0-090 


0-025 


145 


0-100 


0-030 


188 


0-200 


0-035 


235 


0-300 


0-040 


374 


0-400 


045 


539 


0-500 


0-050 


678 




0-055 


807 




. 0-060 


879 




0-065 


899 




0-070 


906 





Pressure in atmospheres. 



906 
896 
869 
850 
671 
562 
456 
364 



TABLE XIII. (Record No. F 70.) 



Cylindrical explosion vessel; charge all in one quarter of cylinder near the recorder; gravimetric 
density 0-0753 ; diameter of cord 0~035 inch (0'89 millim.) ; temperature 17 '0 C. 

Maximum pressure 764 atmospheres (5-01 tons per square inch) ; time required to reach the 

maximum pressure 0'007 second. 



Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


0-001 


76 


0-008 


760 


0-002 


162 


o-oio 


754 


0-003 


241 


0-015 


727 


0-004 


417 


0-020 


694 


0-005 


546 


0-030 


661 


0-006 


724 


0-040 


628 


0-007 


764 


0-050 


595 






0-100 


489 






0-200 


357 






0-300 


265 






0-400 


212 






0-500 


175 



EXPERIMENTS ON SOLID AND GASEOUS EXPLOSIVES. 



397 



TABLE XIV. (Record No. F 71.) 

Cylindrical explosion vessel; charge uniformly distributed; gravimetric density 0-1004 ; diameter of 
cord 0'175 inch (4'45 millims.) ; temperature 17'5 C. 

Maximum pressure 1058 atmospheres (6 '94 tons per square inch) ; time required to reach the maximum 
pressure 0'028 second; charge fired with 2 grammes of fine granulated powder. 



Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


0-002 


26 


0-035 


1058 


0-004 


43 


0-040 


1051 


0-006 


83 


050 


1025 


0-008 


126 


0-060 


998 


o-oio 


162 


0-100 


893 


0-012 


222 


0-200 


727 


0-OH 291 


0-300 


612 


0-016 417 


0-400 


503 


0-018 545 


0-500 


413 


0-020 698 


0-600 


331 


0-022 


843 


0-700 


291 


0-024 


975 


0-800 


248 


0-026 


1038 






0-028 


1058 






0-030 


1058 







TABLE XV. (Record No. F 72.) 

Cylindrical explosion vessel; charge uniformly distributed ; gravimetric density 0'1004 ; diameter of 
cord 0-035 inch (0'89 millim.) ; temperature 17-7' C. 

Maximum pressure 1124 atmospheres (7 -37 tons per square inch); time required to reach the maximum 
pressure 0050 second ; charge fired with 2 grammes of fine granulated powder. 



Time in seconds. Pressure in atmospheres. 


Time in seconds. Pressure in atmospheres. 


0-001 


208 


0-006 


1124 


0-002 519 


0-007 


1107 


0-003 


807 


0-010 


1101 


0-004 


1025 


0-015 


1071 


0-005 


1124 


0-020 


1024 






0-030 


992 






0-040 


959 






0-050 


925 






0-100 


810 






0-200 


645 






0-300 


529 






0-400 


430 






0-500 


363 






0-600 


324 






0-700 


281 






0-800 


248 



398 



MR. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 



TABLE XVI. (Record No. F 73.) 

Cylindrical explosion vessel ; charge uniformly distributed ; gravimetric density 0- 1505 ; diameter of 
cord 0-475 inch (12'07 millims.); temperature 18 C. 

Maximum pressure 1633 atmospheres (10- 71 tons per square inch); time required to reach 

the maximum pressure 058 second. 



Time in seconds. 


Pressure in atmospheres. 


Time in seconds. 


Pressure in atmospheres. 


o-oio 


26 


0-060 


1633 


0-020 


76 


0-065 


1631 


0-025 


126 


0-070 


1587 


0-030 


244 


0-080 


1547 


0-032 


311 


0-090 


1504 


0-034 


413 


0-100 1461 


0-036 


523 


0-150 


1322 


0-038 


665 


0-200 


1207 


0-040 


793 


0-300 


1051 


0-042 


1015 


0-400 


935 


0-044 


1174 


0-500 


843 


0-046 


1332 


0-600 


767 


0-048 


1461 


0-700 


688 


0-050 


1554 


0-800 


628 


0-052 


1603 


0-900 


579 


0-054 


1620 






0-056 


1627 






0-058 


1633 







TABLE XVII. (Record No. F 74.) 

Cylindrical explosion vessel ; charge uniformly distributed ; gravimetric density 0' 1505 ; diameter of 
cord 0-175 inch (4-44 millims.); temperature 17 '6 C. 

Maximum pressure 1749 atmospheres (11-48 tons per square inch); time required to reach 
the maximum pressure 0'023 second. 



Time in seconds. 



Pressure in atmospheres. j| Time in seconds. Pressure in atmospheres. 



)-002 


33 


0-028 


1749 


)-004 76 


0-030 


1742 


)'006 99 


0-035 


1719 


)-008 


162 


0-040 


1692 


)-010 


225 


0-050 


1646 


)-012 


354 


0-060 


1610 


)-014 


545 


0-070 


1564 


1-016 


833 


0-080 


1527 


1-018 


1220 


0-090 


1494 


1-020 


1507 


0-100 


1455 


1-022 


1732 


0-150 


1316 


)-023 


1749 


0-200 


1197 


1-024 


1749 


0-300 


1041 






0-400 


926 






0-500 


853 






0-600 


767 






0-700 


701 



[ 399 ] 



XII. Fifth and Sixth Catalogues of the Comparative Brightness of the Stars in 
Continuation of those Printed in the ' Philosophical Transact ions of the 
Royal Society' for 179fi-91>. 

By Dr. HEESCHEL, LL.D., F.R.S. 

Prepared for Press from the Original MS. Record* by Col. J. HERSOLIEL, 

It.K, F.It.S. 



Received July '24, Read December 7, 190;). 

IN the 86th, 87th, and 89th volumes of the l Philosophical Transactions of the 
Royal Society' for 1796, 1797, and 1799 there appeared a series of four papers 
by Sir WILLIAM (then Dr.) HKRSCHEL containing- the description and results of 
observations made by him of the "Comparative Lustres of Stars" visible to the 
naked eye in northern latitudes. They were arranged in six " Catalogues," of which 
four were actually published, as above. Apparently two more were to have followed, 
containing the remaining constellations. The annexed Tables show the distribution 
of the constellations among the six Catalogues. 

It is not known what prevented the completion of the design at the time. Drafts 
of the intended Fifth and Sixth Catalogues exist among Sir WILLIAM'S papers, 
prepared, as the previous four had been, by Miss CAROLINE HERSCHEL, by abstraction 
from the body of his observations of various kinds, entitled "Abstract of Sweeps and 
Reviews." 

Circumstances which it is unnecessary to detail have now led to the revision (and 
correction where called for) of these drafts and to their publication in the following 
pages, in the same form as those in the earlier volumes. To save reference to the 
latter, the following extract will explain the symbols used to denote relative 
brightness. These are more fully described and illustrated in the pages immediately 
preceding those from which the extract is made, viz., pp. 187-9 of vol. 86. 



"Introductory Remarks and Explanations of the Arrangement and Character* 

" used in the following Catalogue. 

" This Catalogue contains nine constellations, which are arranged in alphabetical 
" order. I have called the present collection the first catalogue. The rest of the 
VOL. CCV. A 398. 2.3.06 



400 DE. HERSCHEL'S FIFTH AND SIXTH CATALOGUES OF THE 

" constellations, which are pretty far advanced, will be given in successive small 
" catalogues as soon as time will permit to complete them. 

" Each page is divided into four columns, the first of which gives the number of 
" the stars in the British catalogue of Mr. FLAMSTEED, as they stand arranged in the 
" edition of 1725. 

" The second column contains the letters which have been affixed to the stars. 

" The third column gives the magnitude assigned to the stars by FLAMSTEED in the 
" British catalogue ; and 

" The fourth contains my determination of the comparative brightness of each star, 
" by a reference to proper standards. 

" All numbers used in the fourth column refer to the stars of the same constellation 
' in which they occur, except when they are marked by the name of some other 
" constellation ; and in that case the alteration so introduced extends only to the 
" single number which is marked, and which then refers to the constellation affixed 
' to the number. 

" The numbers at the head of the notes, which will be found at the end of the 
" catalogue, refer to the stars in the same constellation to which the notes belong. 



" Simple Characters. 

' ' The least perceptible difference less bright. 

" . Equality. 

" , The least perceptible difference more bright. 

"' - A very small difference more bright. 

" -, A small difference more bright. 

- A considerable difference more bright. 
- Any great difference more bright in general. 



" Compound Characters, expressing the Wavering of Star Light. 

" '. From the least perceptible difference less bright to equality. 

" ; From equality to the least perceptible difference more bright. 

" ~ From a very small difference more bright, to the least perceptible difference. 

"' =, From -, to - &c. 

" -The wavering expressed by the passing of the light from a state of the least 
' perceptible difference less bright to equality, and to the least perceptible difference 
' more bright. 

" T The wavering expressed by the changes from - to , and to . or from . to and 
<l to - " 



COMPARATIVE BRIGHTNESS OF THE STARS. 
DISTRIBUTION of Constellations in Catalogues. 



401 



An 

Aq 

Al 

AT 

An 

Bo 

Cm 

Cc 

Cv 

Ca 

Ci 

C P 

Cs 

On 

Ce 

Ct 

Co 

Cl) 

Cr 



Constellation. 



Andromeda . 
Aquarius . 
Aquila . 
Aries 

Auriga . . . 
Bootes. 

Camelopardalus 
Cancer . 
Canes venatiei 
Canis major . 
Canis minor . 
Capricornus . 
Cassiopeia . . 
Centaurus . 
Cepheus 
Cetus . . . 
Coma Berenices 
Corona borealis 
Corvus . 
Cygnus. 
Delphinus . 
Draco . . . 
Kquuleus . 



Erianus 
Gemini . 



Dl 
Dr 

I? 

Gm 

Hr Hercules . 

Hy Hydra . . . . 

IIC Hydra et Crater 

Lc Lacerta 

La Leo major . 

Li Leo minor. 

Lp Lepus . . . . 

Lb Libra . . . . 

Lu Lupus . . . . 

Lx Lynx . . . . 

Ly Lyra . . . . 

Mn Monoceros 

Na Navis . . . . 

Or Orion . . . . 

Pg Pegasus . . . 

Pr Perseus . . . 

Ps Pisces . . . . 

Pa Piscis austrinus . 
Sagitta .... 

Sr Sagittarius 

So Scorpio. 

Ss Serpens 

St Serpentarius . . 

Sx Sextans . . . 

Ta Taurus. . . . 

Tr Triangulum . . 

Ua Ursa major . 

Ui Ursa minor . 

Vr Virgo . . . . 

VI Vulpecula. . . 



Catalogue Number. 



III. 

1. 

I. 

II. 

IV. 

III. 

V. 

III. 

VI. 

II. 

II. 

I. 

II. 

III. 

III. 

IT. 
VI 
III. 
II. 

1. 

I. 
IV. 

I. 

II. 

11. 

I. 

V. 

V. 

in. 
11. 
v. 
in. 

VI. 
VI. 
IV. 
IV. 
IV. 

in. 

in. 

i. 

IV. 

v. 

VI. 

I. 

V. 
VI. 
VI. 
VI. 
IV. 
IV. 
IV. 
VI. 
V. 
VI. 
V. 



Number of stars in 
constellation. 



66 
108 
71 
66 
66 
54 
58 
83 
25 

31 
ii 

51 

55 

5 

35 

97 

4.", 

21 

9 

81 
18 
80 
10 
09 
85 

113 
60 
31 
16 
95 
53 
19 
51 
5 

45 
21 
31 
2-2 
78 
89 
59 

113 
24 
18 
65 
35 
64 
74 
41 

141 
16 
87 
24 

110 
35 



VOL. CCV. A. 



3 F 



402 



DR. HERSCHEL'S FIFTH AND SIXTH CATALOGUES OF THE 
NUMBER of Stars Catalogued. 



CATALOGUE I. 


Number of stars. 


CATALOGUE IV. 
Auriga 


Number of stars. 


108 
71 
51 
81 
18 
10 
113 
89 
18 


66 
80 
45 
21 
31 
59 
41 
141 
16 




Draco . 




Lynx 




Lyra 


Cygnus 


Monoceros 




Perseus 




Sextans 


Pegasus 




Triangulum 






CATALOGUE II. 

Aries 
Canis major 
Canis minor 


66 
31 
14 
55 

97 
9 
69 
85 
95 


CATALOGUE V. 
Camelopardalus 


58 
60 
31 
53 
113 
65 
24 
35 


Hydra et Crater .... 


Leo minor 


Cctus 


Pisces 


Sagittarius 


Eridanus 


Ursa minor 
Vulpeculu 


Leo 




CATALOGUE III. 

Andromeda 
Bootes 
Cancer 


66 
54 
83 
5 
35 
21 
16 
19 
22 
78 


CATALOGUE VI. 
Canes venatici 


25 
43 
51 
5 
24 
35 
64 
74 
87 
110 


Coma Berenices 


Libra .... 


Centaurus 


Lupus 


Cepheus 


Piscis austrinus 


Corona borealis 
Lacerta 


Scorpio 


Serpens .... 


Lepus .... 


Serpentarius .... 


Navis 


Ursa major 
Virso 


Orion 





COMPARATIVE BRIGHTNESS OF THE STARS. 

CATALOGUE V. 
FIFTH CATALOGUE OF THE COMPARATIVE BRIGHTNESS OF THE STARS. 



403 









Lustre of the Stars in Camelopardalus. 


1 




6 


3. 1 


2 




5 


2.3 7-2 


3 




6 


2.3.1 


4 




6 


7 - 4 , 5 


5 




6 


4,5-8 


6 




6 


8 , 6 


7 




5 


779 Aur 7-2 7-, 8 7-, 4 


8 




7 


7-8 5-8,6 


9 




4.5 


10, 9 


10 




5.4 


33 Aur ; 10 10 , 9 


11 




5 


11 , 9 Aur 


12 




6 


9 Aur -, 12 


13 




4.5 


Does not exist 


14 




5 


17 , 14 , 19 


15 




6 


30 Aur (32) , 15 


16 




6 


16 . 30 Aur (32) 


17 




6 


31 , 17 , 30 17 , 14 


18 




6 


24; 18 


19 




6 


14, 19 


20 




7 


22 . 20 


21 




6.7 


30 , 21 . 23 


22 




7.8 


24 , 22 . 20 28 . 22 


23 




6 


21 . 23 


24 




6 


26 . 24 , 22 20 ; 18 


25 




7.8 


25 . 34 


26 




5.6 


26. 24 


27 




5.6 


Does not exist 



3 F 2 



404 



DR. HERSCHEL'S FIFTH CATALOGUE OF THE 



Lustre of the Stars in Camelopardahis continued. 


28 




6.7 


29 , 28 . 22 


29 




5.6 


29 , 28 


30 




6 


31-30 17 , 30 , 31 


31 




5 


30 Aur (32) - 31 - 30 31 , 17 37 , 31 -, 38 


32 




5 


32 - - 33 16 . 30 Aur (32) , 15 30 Aur (32) - 31 42 . 30 Aur (32) 


33 




7 


32 - - 33 . 34 


34 




6 


33 . 34 25 . 34 34 ; 35 


35 




5.6 


34 ; 35 


36 




6 


42 , 36 


37 




5.6 


37 , 31 37 , 40 


38 




7 


31 -, 38 


39 




6.7 


40- 39 


40 




6.7 


37 , 40 - 39 


41 




7 


8 Lyn , 41 - 10 Lyn 


42 




4.5 


43 ; 42 . 30 Aur (32) 43 , 42 , 36 


43 




4.5 


43 ; 42 43 , 42 


44 




6 


46 ; 44 7 45 


45 




7 


44 , 45 


46 




7 


47 , 46 ; 44 


47 




6 


18 Lyu , 47 , 46 


48 




6 


56 - 48 


49 




5 


51 , 49 


50 




6 


27 Lyu - 50 


51 




5 


55 -, 51 , 49 


52 




5 


58 - 52 - 54 


53 




6 


53 ,56 57 . 53 


54 




6 


52-54 


55 




5 


55 -, 51 



COMPARATIVE BRIGHTNESS OF THE STARS. 



405 



Lustre of the Stars in Camelopardalus continued. 


56 




6 


29 Lyn - 56 58 , 56 53 , 56 56 - 48 


57 




5 


58 . 57 57 . 53 


58 


5 


29 Lyn , 58 , 56 58 . 57 58 - 52 


Lustre of the Stars in Hydra. 


1 




4 


1 ,2 


2 




4 


1 , 2 - 10 


3 




6 


15 ; 3 17 


4 


8 


4 


22 , 4 . 7 4.12 35 ; 4 , 31 


5 


(T 


5 


7,5 13 . 5 , 18 


6 




6 


9. 6 


7 


>/ 


4 


4.7,5 7,13 


8 




6 




9 




6 


22 . 9 . 6 


10 




5 2 10 


11 





4 


16 , 11 16-, 11 -22 4Ci"it.ll ll,4Civit 


12 




6 


4 . 12 


13 


P 


5 


7,13. 5 


14 




5.6 


18 . 14 


15 




6 


15 ; 3 


16 





4 


16 -, 11 17 Leo , 16 , 11 


17 




6 


3-17 


18 


ia 


6 


5 , 18 . 14 


19 




6 19-20 27 - 19 - 20 23 ; 19 , 21 


20 




6 


19 - 20 . 24 19 - 20 


21 




6 


19 , 21 


22 


e 


4 


11 - 22 , 4 22 . 9 


23 




6 


23; 19 



406 



DR. HERSCHEL'S FIFTH CATALOGUE OF THE 









Lustre of the Stars in Hydra continued. 


24 




6 


20 . 24 - 29 24 - 25 


25 




6 


24-25 


26 




6 


27 -26 


27 




6 


27 - 19 27 - 26 


28 


A 


6 


28 . 33 


29 




6 


24-29 


,30 


OL 


2 


46 Or - 30 - 53 Or 


31 


T 1 


5 


4 , 31 ; 32 


32 


T" 


5 


31 ; 32 15 Sext - 32 32 - 30 Sext 


33 




6 


28 . 33 


34 




6 


27 . 34 -, 36 


35 


/, 


4 


35 ; 4 35 , 15 Soxt - 32 


36 




6 


34 -, 36 


37 




6 


37 . 34 


38 


K 


4.5 


407 38 


39 


1) 


5 


41 -, 39 -, 40 


40 




U" 


5 


39 -, 40 , 38 


41 


X 


4 


41 -, 39 4 Crat -, 41 


42 


/' 


4 


2 Crat - - 42 . 43 42 , 7 Crat 


43 


p 


5 


42 . 43 . 1 Crat 1 Crat -, 43 1 Crat - - 43 


44 




6 


44 , 3 Crat 


45 


* 


6 


8 Corvi - 45 


46 


y 


3 


7 Corvi = , 46 46 7 49 


47 




6 


47 - 48 


48 




6 


47-48 


49 


TT 


4 


46 7 49 49 - 20 Lib 


50 




6 


52 , 50 50 -, 1 Lib 


51 




5 


51 , 52 



COMPARATIVE BRIGHTNESS OF THE STARS. 



407 









Lustre of the Stars in Hydra continued. 


52 




5 


51 , 52 , 50 


53 




6 


58 . 53 , 56 4 Lib .56 54-4 Lib 


54 




5.6 


54 , 58 6 Lib - 54 - 4 Lib 


55 




6 


57 . 55 . 59 57 7 55 -, 3 Lib 12 Lib , 55 - , 3 Lib 


56 




6 


53 , 56 . 57 4 Lib . 56 . 57 


57 




7 


56 . 57 . 55 56 . 57 , 55 


58 




5 


54 , 58 . 53 6 Lib - 54 


59 




6 


55 .59-60 


60 




6-7 


59 - 60 








Lustre of the Stars in Hydra et Crater. 


1 


& 


6 


43 Hy . 1 3 . 1 -, 43 Hy I - - 43 lly 2 -, 1 3,1 


2 


</> 


5 


2 - - 42 Hy 2-3 2,1 2-3 


3 


Ji 


6 


2-3.1 3 ,13 44 Hy , 3 2-3,1 3,6 


4 


J' 


4 


4 . 11 Hy 4-12 4 ; 9 Corvi 4 -, 12 4 -, 41 Hy 1 1 lly , 4 


5 


&s 


G 


6,5 


6 


i 


6 


3,6,5 13-6 


7 


a 


4 


42 Hy , 7 15 , 7 . 11 


8 


i 


6 


10-8 


9 


X 


5 


9 , 10 


10 




6 


9 , 10 - 8 


11 


P 


3.4 


7 . 11 


12 


s 


4 


4-12-15 4 -, 12 12 -, 15 


13 


A 


5.6 


3, 13 13-6 27 , 13 , 30 


14 


e 


4 


21 - 14 - 24 


15 


y 


4 


12 - 15 12 -, 15 , 7 


16 


K 


5 


24- 16 


17 




6 


19-, 17 ,18 31 . 17 . 29 



40H 



DE. HERSCHEL'S FIFTH CATALOGUE OF THE 



Lustre of the Stars in Hydra et Crater continued. 


18 




6 


17 ,18-26 28, 18 


19 





4 


19 - 17 


20 




6 


26 7 20 , 23 25 . 20 


21 


e 


4 21-14 


22 




7 


23 . 22 


23 




6 


20 23 23 . 22 


24 


< 


5 


14 - 24-- 10 


25 


i) 


5 


25 . 20 


26 


- 


6 


18 - 26 , 20 


27 


i 


4 


27 , 13 


28 


ft 


4 


28 , 18 


29' 




6 


17 . 29 


30 


v 


4 


13, 30 . 31 


31 




5.6 


30 . 31 . 17 


Lustre of the Stars in Leo minor. 


1 


1 ' 


1,4 5,1 


2 


^ 


6 


3 . 2 


3 


o 

-u 

F-3 


6 


4-3.2 3.0 


4 


03 
CO 

c 


7 


1,4-3 


5 


X 


7 


5, 1 


6 


-4-3 


6 


3. 6 


7 


5 


6 


8,7 19 Urssemaj , 7 


8 


i" 


5 


8,7 11.8 8-19Urssemaj 


9 


0> 

s 


6 


9 Leonis maj ,9.13 Leonis imij 


10 


O 


4.5 


39 Lyncis-, 10 -, 11 


11 


5- 


6 


10-, 11.8 11-13 


12 




5 


13. 12 



COMPARATIVE BRIGHTNESS OF THE STARS. 



409 









Lustre of the Stars in Leo minor continued. 


13 




6 


11 - 13 .12 


14 




6 


42 Lyncis 14 


15 




6 


15 . 42 Lyncis 


16 




6 


17 , 16 


17 




6 


19-- 17 , 16 


18 


i 


6 


20 - - 18 


19 




5.6 


19-- 17 


20 




6 


21 __ 20 -- 18 


21 




5 


31 ; 21 - - 20 


22 


o 


6.7 


24- 22 


23 


o 
V> 
ee 


5.6 


23 -, 24 


24 


$ 
= 


6 


23 -, 24 - 22 


25 


o 

O 

E 


6 


47 , 25 


26 


^a 

+3 

g 


6 


27 - 26 . 29 


27 


o> 
> 


6 


28 . 27 - 26 


28 


~L 

0> 
ti 
^ 


6 


30 - 28 . 27 


29 


:Q 
(H 
0) 
43 


6 


26 . 29 


30 


4?5 
O 

O 


5.4 


30-28 


31 


fc. 


5 


31 ; 21 


32 




6 


38, 32 


33 




4.5 


42, 33 


34 

I 




4.5 


34 -, 36 34 - 35 


35 




5.6 


34 - 35 , 36 


36 




6 


34 -, 36 35 , 36 


37 




3 


37 -42 


38 




6 


38, 32 


39 




6 


40-39 


40 




6 


41 -, 40 - 39 40 - 44 



VOL. CCV. A. 



3 G 



410 



DE. HEESCHEL'S FIFTH CATALOGUE OF THE 









Lustre of the Stars in Leo minor continued. 


41 




5 


41 -, 40 41 - 53 41 - 52 Leonis mcij 


42 




4.5 


37 - 42 , 33 42 , 44 


43 


2 

.2 


6 


44 ; 43 _ _ 45 44 ; 43 - 45 


44 


c8 

"3 


6 


40 - 44 , 43 42 , 44 ; 43 


45 


m 
C 



6 


43 _ _ 45 43 - 45 


46 


CO 

J3 

43 


4.5 


36 Leonis maj - 46 , 24 Leonis maj 


47 


_g 


6 


46 Leonis maj - 47 47 , 25 46 Ursse maj -, 47 


48 


> 

a 


6 


48 , 50 


49 


^i 

rt 
r 


6 


51 Leonis maj 49 


50 


> 
49 
4J 
O 


6 


48 , 50 50 , 52 


51 


o 

g. 


6 


52 ,51 52 , 51 


52 




5.6 


53 --52, 51 50,52,51 


53 




5-6 


41 _ 53 _ _ 52 








Lustre of the Stars in Pisces. 


1 




7 


2.1-3 


2 




6 


5,2.1 


3 




6 


1 - 3 


4 


ft 


5 


4,5 


5 


A 


6 


4,5,2 7.5 


6 


7 


4 


67 28 


7 


6 


5.6 


10, 7 . 5 7-16 19 . 7 7-32 7 ; 34 


8 


*i 


5 


9--8 


9 


K 2 


7.6 


9--8 


10 


6> 


5 


10 , 7 18 . 10 


11 




6 


14,11 ,12 


12 




6 


11 , 12 , 13 


13 




6 


12, 13 



COMPARATIVE BRIGHTNESS OF THE STARS. 



411 



Lustre of the Stars in Pisces continued. 


14 




6 


14, 11 


15 




6 


16- 15 


16 




6 


7 - 16 - 15 


17 


t 


6 


28,17 17,18 


18 


A 


5 


17 , 18. 10 


19 




5 


19. 7 


20 




5.6 


27 , 20 , 24 


21 




6 


21 . 22 


22 




C 


21 . 22 - 25 


23 




6 


23 - 83 Pegasi 


24 


6 


20 , 24 


25 




6 


22 - 25 


26 


6 28 - - 26 


27 




5 


29 . 27 , 20 


28 


CO 


5 


6 7 28 - - 26 28 , 17 


29 




5 


30 - 29 . 27 


30 




5 


33 . 30 - 29 


31 


f 1 


6 


32 , 31 


32 


c- 


5-6 


7 -32 , 31 


33 




4 33 . 30 


34 




6 


7 ; 34 


35 




6 


41 , 35 , 36 35 , 51 


36 




6 


35 , 36 , 38 


37 




6 


39 ,37 42 , 37 43 7 37 


38 




7 


36 , 38 - 45 


39 




6 


40 ; 39 40 ; 39 , 37 


40 




6 


40 ; 39 40 ; 39 


41 


d 


6 


41 , 35 



3 G 2 



412 



DR. HERSCHEL'S FIFTH CATALOGUE OF THE 









Lustre of the Stars in Pisces continued. 


42 




6 


43 . 42 , 37 42 ; 43 


43 




6 


43 .42 44 , 43 42 ; 43 ~ 37 


44 




6 


44 ,43 44 - 10 Ceti 


45 




6 


38 - 45 


46 




6 


52 -, 46 


47 




6 


47 . 52 47 - 48 


48 




6 


47 - 48 . 49 48 -, 49 


49 




6 


48 . 49 , 53 48 -, 49 


50 




6 


See note at foot as to this number and 55 


51 




6 


35 , 51 


52 




6 


47 . 52 -, 46 56 , 52 , 54 See footnote 


53 




7 


49 , 53 


54 




6 


56 7 54 52 , 54 , 61 54 , 59 


55 




6 


See note at foot 


56 




6 


56 ,54 56 , 52 See footnote 


57 




6 


58 ; 57 58 ; 57 


58 




7 


58 ; 57 64 - 58 ; 57 


59 




6 


54,59,61 66.59 66-59 61 


GO 




6 


62 . 60 


61 




7 


54 , 61 59 ,61 59 - 61 


62 




6 


63 -, 62 . 60 


63 


8 


4 


63 , 62 


64 




6 


64 - 58 64 - 66 


65 


i 


6 


65 . 68 


66 




6 


64 - 66 . 59 66 59 


67 


k 


6 


68 , 67 


68 


h 


6 


65 . 68 , 67 


69 


o-l 


5 


83 , 69 . 82 






COMPARATIVE BRIGHTNESS OF THE STARS. 



41. S 









Lustre of the Stars in Pisces continued. 


70 




6 


Does not exist 71 - 70 


71 





4 


71-86 71- -70 


72 




6 


81 , 72 - 75 72 , 87 


73 




6 


77 , 73 , 88 


74 


* 


5 


74 , 84 


75 




G 


72 75 


76 


<r-' 


5 


78 . 70 


77 




6 


80 - 77 , 73 


78 




6 


82 - 78 . 76 


79 


f2 


6 


84 - 79 ; 81 


80 





5 


80-77 


81 


^3 


6 


79 ; 81 , 72 


82 


g 


6 


69 . 82 - 78 


83 


T 


5 


83 , 69 s:i ; 90 


84 


X 


5 


74 , 84 - 79 


85 


4- 


5 


90 . 85 


86 


C 


4 


71 -, 86 86 , 89 


87 




7 


72 , 87 


88 




6.7 


73 , 88 


89 


/ 


6 


86 , 89 


90 


U 


5 


83 ; 90 - 91 90 , 95 90 . So 


91 


I 


6 


90 - 91 95 , 91 


92 




7 


97 , 92 


93 


p 


5 


93 . 94 


94 




5 


93 . 94 - 97 94 , 107 


95 




7 


90 , 95 , 91 96 , 95 


96 




6.7 


96 , 95 


97 




6.7 


94 - 97 , 92 



414 



DK. HERSCHEL'S FIFTH CATALOGUE OF THE 



Lustre of the Stars in Pisces continued. 


98 


/* 


5 


51 Ceti (106) , 98 106 - 98 


99 


n 


4 


99 , 5 Arietis 2 Trianguli - 99 - 5 Arietis 


100 




6 


102 -, 100 101 , 100 101 - 100 , 104 


101 




6 


101 -,104 105,101,103 102-101,100 102-101-100 101.105 


102 


7T 


5 


102 -, 100 102 - 101 107 , 102 - 109 102 - 101 


103 




8.7 


101 , 103 105 , 103 , 104 


104 




6.7 


101 -, 104 100,104 103,104 


105 




6.7 


105 , 101 101 . 105 , 103 


106 


V 


5 


110-106,98 110-106-98 111,106-112 


107 




6.7 


107 , 102 94 , 107 - - 109 


108 




6 


Does not exist 


109 




8 


102 - 109 107 - - 109 


110 


O 


5 


110 - 51 Ceti (106) 5 Arietis -,110 110 - 106 


111 


* 


6 


111 , 106 


112 




6.7 


106 -, 112 


113 


a 


3 


113 , 5 Arietis 


[NOTE to 50, 52, 55, 56. The following entries occur : January 1, 1796, " Either 50 or 52 is wanting. 
By 46 it is 52 that is wanting "...." 56 is wanting." On the same date are comparisons involving 
50 and 55, to which asterisks are affixed, referring to si footnote, in W. H.'s hand and obviously of 
later date, "* As it appears by Index that 50 and 55 have no observation, put 52 and 56 for 
them." In drawing up Catalogue V, C. L. H. has evidently done this, adding, however, " does not 
exist " opposite 50 and 55, which is, perhaps, hardly warranted. With this exception, the same 
substitutions have been made in this Abstract- -though the reason is not clear. J. H.] 

[108 is shown to be (by an error of FI.AMSTEED'S, transferred to the Atlas) the same as 109, but 3 
out of place.] 


Lustre of the Stars in Sagittarius. 


1 




6 


33 Scorpii , 1 


2 




6 


2 , 52 Ophiuchi 


3 


P 


6 


51 Ophiuchi - 3 






COMPARATIVE BRIGHTNESS OF THE STARS. 



415 









Lustre of the Stars in Sagittarius continued. 


4 


h 


6.7 


7.479 


5 


i 


7 


5,7 5 . 12 


6 




7 


54 Ophiuchi -6.8 


7 


a 


6 


5,7.4 12 , 7 


8 




7 


6.8 8 does not exist 


9 




7 


479 


10 


y 


3 


19- , 10 


11 




7 


Does not exist 


12 




7 


5 . 12 , 7 


13 


/"' 


4 


27 , 13, 40 39 - 13- , 15 13 -, 21 


14 




7 


15 , 14 . 16 


15 


1* 


6 


13- 7 15 , 14 21 7 15 


16 




7 


14 . 16 - 17 


17 




7 


16 - 17 


18 




7 




19 


s 


3 


38 . 19, 27 22 7 19 ; 20 19 = 7 10 


20 





3 


19 ; 20 


21 




6 


21 7 15 13 -, 21 


22 


A 


4 


41 . 22 , 38 22 ~ 19 


23 




7 


25-23 


24 




7 


24 -, 26 


25 




7 


26 , 25 25 - 23 


26 




6 


24 -, 26 , 25 


27 


4> 


5 


19 , 27 , 40 27 ,36 27 , 13 


28 




7 


28-31 


29 




6 


36 , 29 , 33 


30 




6 


33 , 30 . 31 31 , 30 


31 




6 


30 . 31 28 31 , 30 



416 



DR. HKRSCHEL'S FIFTH CATALOGUE OF THE 









Lustre of the Stars in Sagittarius continued. 


32 


r 1 


5 


32 ; 35 


33 




6 


35 - 33 , 30 29 , 33 


34 


IT 


4.3 


34 _. -41 34~_4i 50 Aquilse , 34 . 33 Capricorni 


35 


l'- 




32 ; 35 35 33 


36 


? 




27 , 36 , 39 37 - 36 36 , 29 36 , 39 


37 


f 


6 


37 - - 36 


38 


f 


3 


22 . 38 . 19 


39 





4 


36 , 39 36 , 39 39 . 44 39 - 13 


40 


T 


4 


27 , -10 13 , 40 


H 




4 


34 11 >> it 41 










42 


^ 


5 


42, 49 


43 


rf 


6 


46-43 . 45 


14 


P 1 


5 


39 . 44 -, 46 


45 


r' 


(i 


43 ; 45 50 ; 45 


46 


t> 


G 


44-, 46 - 43 


47 


X 1 


5 


47 - - 48 47 ; 49 


48 


X 2 


5 


47 -48 


49 


x 3 


6 


47 ; 49 42 , 49 


50 




6 


50 ; 45 


51 


A 1 


6 


52-51 51 , 53 . 53 


52 


A 


6 


52 - 51 


53 




6 


51 , 53 . 53 


54 


e 1 


6 


55 ; 54 . 61 


55 





6 


55 ; 54 


56 


/ 


6 


56 -, 57 


57 




6 


56 -, 57 


58 


(0 


5 


62, 58 . 60 


59 


6 


5 


60, 59 



COMPARATIVE BRIGHTNESS OF THE STARS. 



417 









Lustre of the Stars in Sagittarius continued. 


60 


a 


5 


58 . 60 , 59 


61 


9 


6 


54. 61 


62 


c 


6 


62, 58 


63 




6 


63-64 


64 




6 


63 - 64, 65 


65 




6 


64,65 


Lustre of the Stars in Ursa minor. 


1 


a. 


3 


7 ; 1 - 14 Draconis 1,7 a (1) - /3 (7) Polaris (1) '. 7 1,7 
1-7 1-7 1-7 a. (50) UrsiB maj 7 1 7 7 1,7 


2 




6 


Is wanting 


3 




6 


4-3 


4 


b 


5 


5-4 4-3 


5 


a 


4 


22-5-4 


6 




7 


11 - -6 9-6 


7 


ft 


3 


7 ; 1 l,7,y ( 33 ) Draconis 1-7 50 Ursie maj , 7 50 Ursce maj f 7 
1 f 7 7 , 50 Ursa? maj 1,7 1-7 1-7 50 Ursa: maj '. 1 
1-7 IT? 79 Ursse maj ,'7 7-64 Ursse maj 7 - 33 Draconis 
1,7 


8 




6 




9 




7 


9-6 9, 10 


10 




7 


9 , 10, 14 14 . 10 


11 




5 


13__ 11 __ 12 11 --6 


12 




7 


11 -- 12 12 . 8 . 8 


13 


y 


3 


13- - 11 


14 




7 


10, 14 14. 10 


15 


e 


5 


16-15 16-15 15 --18 


16 


t 


4 


16-15 16-15 


17 




7 


19-17, 20 


18 




6 


15-- 18 



VOL. CCV. A. 



3 H 



418 



DE. HEESCHEL'S FIFTH CATALOGUE OF THE 



Lustre of the Stars in Ursa minor continued. 


19 




5 


21 , 19. 20 21 , 19- 17 


20 




6 


21 - 20 19 . 20 17 , 20 


21 


'/ 


5 


21 -20 21 , 19 21 , 19 


22 


t 


4 


22-5 


23 


S 


3 


23 -, 24 


24 


6.7 


23 - 24 


Lustre of the Stars in Vulpecula. 


1 




5 


1 - 1 Sagittie 1-2 1 -, 2 


2 




6 


1-2,1 SagittiB 1 -, 2 , 1 Sagittse 


3 




6 


6-3,3 Cygni 3 - - 3 Cygni 3 - - 3 Cygni 


4 




G 


9,4.5 


5 




6 


4.5,7 


6 




4 


G-- 8 G- 3 


7 




5 


9-7 5,7 


8 




G 


G - - 8 8.3 Cygni 8 . 3 Cygni 


9 




6 


5 Sagittaj -9,8 SagittiB 9-7 9,4 9-10 14-9 


10 




6 


9- 10, 13 10-- 11 13-- 10 10, 14 


11 






10-- 11 


12 




5 


13 - 12 -, 14 


13 




6 


10,13 13-12 13 --10 16,13.17 


14 




5 


14-9 12-, 14 10,14 


15 




4.5 


15 , 23 


16 




5 


16, 13 


17 




4.5 


13.17 17.22 


18 




6.5 


19 . 18, 20 


19 




6 


19 . 18 


20 




5.6 


18, 20 



COMPARATIVE BEIGHTNESS OF THE STARS. 



419 



Lustre of the Stars in Vulpecula continued. 


21 




5.6 


23 , 21 -, 24 


22 




5 


17 . 22 


23 




4.5 


15 , 23 , 21 


24 




5 


21 -, 24 24 . 25 


25 




6 


24. 25 


26 




6 


27, 26 


27 




5 


27, 26 


28 




6 


29 . 28 . 32 


29 




5 


31 , 29 . 28 


30 




6 


32 . 30 


31 


r 


6 


31 , 29 


32 


2 


5 


28 . 32 . 30 35 . 32 


33 




6 


33-34 


34 




6 


33-34 


35 




6 


35 . 32 



3 H 2 



420 DK. HEKSCHELS FIFTH CATALOGUE OF. THE 



NOTES. 

r N.B. A long dash between two notes or remarks under the same number indicates 

that they are disconnected, and occur at an interval of time of days or months 
even } n the course of the " reviews." The only connecting link is the number 
of the star to which they refer. J. H.] 

Notes to Camelopardalus. 

8 Is not in the place where it is marked in Atlas : the RA should be + to make it 
agree with a star that is thereabout, or to make it agree with another. Either of 

them will be 7 -, 8. The star following 7 and 8, observed by FLAMSTEED, p. 286, 

is in its place, but is much less than 6m. I should call it 8m. 

9 Has no time in FLAMSTEED'S observation. It seems to be placed in Atlas 
considerably too late, so as perhaps to require a correction 10' in time. 

13 Does not exist. 13 does not exist. My double star VI, 35, is 9 Aurigee. 

17 The time in FLAMSTEED'S observation is marked " circiter," but I find that my 
viewing instrument cannot, for want of other near stars, determine whether it is 
properly placed in the Atlas and catalogue. 

27 Does not exist. FLAMSTEED never observed it. 27 28 There is an obser- 
vation by FLAMSTEED, p. 286, on a star S. of 28, but it does not exist, nor 27. 
27 is wanting. A star observed by FLAMSTEED, p. 286, is not in the place where it 
should be. 27 was never observed by FLAMSTEED. 

32 Is the same with 30 Aurigse. The stars 32 33 34, as I have called them, 

Oct. 30, are small stars nearly in a line, but I doubt whether my 32 is FLAMSTEED'S 
star. The Atlas does not give it as it is in the heavens. The star taken for 32 
Cam. is a small star between 33 and 30 Aurigae, not given in any catalogue. 

35 Has no time, but seems to be very properly placed in Atlas and catalogue. 

39 My instrument will not determine its place. It is without time in FLAMSTEED'S 
observation. 

42 A star observed by FLAMSTEED, p. 288, who calls it 4m, preceding 42 and 43 is 
in its place. 

45 and 46 By FLAMSTEED'S observations should have their PD reversed, but in the 
heavens they seem to stand as they are placed in Atlas and catalogue. 

49 I cannot determine the time of 49, which FLAMSTEED'S observations have : : 

52 54 58-52-54 but I am not quite sure of 52 and 54. There are so many 
small stars, that it is not possible without fixed instruments to ascertain them 

positively. 54 in FLAMSTEED'S observations by strias (screws) requires PD-2, 

but it is not possible to ascertain its place positively. 



COMPARATIVE BRIGHTNESS OF THE STARS. 421 

Notes to Hydra. 

8 There is but one star, which if it be 31 Monocerotis, then 8 is not there. 
FLAMSTEED never observed it. 

36 Is not in the place where it is marked in Atlas. The time in FLAMSTEED'S 
observations is marked : : 

43 Is hardly visible in my small telescope. -1 Crateris - - 43 . Dec. 15, 1795, 
it is 43 Hydrse . 1 Crateris, but now (Jan. 26, 1797) it is 1 Crateris - - 43 Hydra. 
I suppose 43 to be changeable. 

Notes to Hydra et Crater. 
1 See note to 43 Hydrse, above. 

22 I cannot see 22 in the place where FLAMSTEED has given it, but 1 above is a 
star which I suppose is it ; calling that, therefore, 22, it is 23 . 22. 

Notes to Leo minor. 

12 Near 12 is a star observed by FLAMSTEED, p. 438. 12 wants a correction 
+ in EA. 

17 Kequires -10' in PD. 

22 Is not to be seen. 23 -, 24 - 22. There is a star pointed out by 23 and 24 
which may be 22, but then its situation is faulty about 30', being too far from 28. 

32 The star north of 32 observed by FLAMSTEED, p. 220, is in the place. 

41 54 54, /3 Leonis, and the star in Leo minor's tail-end, 41 Leo minor, are in 
succession of magnitude. 

49 Is a very small star, and a much larger between 49 and 60 Leonis major is not 
down in catalogue and Atlas. 

Notes to Pisces. 

1 Which has the time " circiter" in FLAMSTEED seems to be placed in Atlas and 
in the catalogue a little later than it should be ; perhaps 5' or 6' of space. 

40 ; 39 A larger star than either is 1 4' towards a Androm. If this was mistaken 

for 39 perhaps it might give rise to the supposition of the loss of 40. 40 is 

not lost. 

48 Has no time. In the heavens it seems to be nearly in the place where the 

catalogue gives it. -48 -, 49. The observation 48 . 49, Jan. 1, 1796, is probably 

owing to a mistake of the star, as there is one nearly equal to 48 near it which is not 
in FLAMSTEED'S catalogue nor Atlas. 

50 52 56 Either 50 or 52 is wanting. By 46 it is 52 that is wanting ; 56 is 
wanting. [Note by W. H. : "As it appears by Index that 50 and 55 have no 
observations, put 52 and 56 for them."] 

59 FLAMSTEED has no observation of 59, but there is a star in the place where the 
catalogue gives it. 



422 DE. HERSCHEL'S FIFTH CATALOGUE OF THE 

70 Does not exist. 70 is a very small star. FLAMSTEED observed it, p. 406. 

71 Is so small that it may, perhaps, not be FLAMSTEED'S star, but there is no other. 

72 A star between 72 and 78, observed by FLAMSTEED, pp. 149, 180, is in its place. 
It is = 72 nearly. 

104 Is 8 lower than 1 Arietis (which does not exist) is marked ; perhaps it was by 
mistake placed 8 more north and called 1 Arietis. 

108 Does not exist, or is invisible. -There is a large star l from 6 Arietis and 
2| from 107, not in Atlas. -108 does not exist. 109 is just 3 south of it and is, 
perhaps, the same. On p. 332 of FLAMSTEED'S observations the number is cast up 
3 wrong, which has produced 108 Pise. The observation belongs to 109. 

Notes to Sagittarius. 

I FLAMSTEED has no observation of 1, but there is a star exactly in the place 
where 1 is marked in the Atlas. 

8 Does not exist. There is a small star at rectangles to 17 15 13 towards the 
place where 8 is marked in the Atlas, but it is much too near 13 to be 8. 

I 1 Does not exist. 

12 The RA of 12 requires a correction of about 1 minus, for in the place where 12 
is marked in Atlas is no star, but 1 before there is one which answers to it. 

14 The star observed by FLAMSTEED, p. 171, is in its place ; it is lj S. of 14. 

181 see many small stars north of 19, but cannot see 18 south of it. 18 is 
not in the place assigned by FLAMSTEED'S catalogue, but about 1 more in RA is a 
star which is probably the one intended. It was observed by FLAMSTEED, p. 115. 

23 24 The star between 25 and 26 north of them observed by FLAMSTEED, p. 374, 
is in its place. 23 does not exist. There is a star that answers pretty well to 23. 
It is a little farther from 25 than it is laid down in Atlas. 24 should be nearer to 25 
than in Atlas. The observation of FLAMSTEED, p. 532, gives it right. 

53 Is double, and I cannot say which is FLAMSTEED'S star. 

Notes to Ursa minor. 

1 appears uncommonly bright. -The pole star seems to be decreased, or ft is 

increased. The place of the moon may possibly influence appearances -a , ft The 

night is not favourable. Very clear, a. - ft. 

2 Is not as in Atlas, or rather it exists not. FLAMSTEED observed a star, 

pp. 213, 214, 215, which has been misplaced and called 2 Ursa minor. It should be 
2 further from 1, and it is in the place where it was observed. 

4 By FLAMSTEED'S observation the RA of 4 should be - 3 50' in time ; but 
without a fixed instrument I cannot perceive that 4 is misplaced, being so near 
the pole. 

8 Either exists not, or is at least not in the place marked in Atlas. 8 is 



COMPAEATIVE BRIGHTNESS OP THE STABS. 423 

misplaced in Atlas: there are two small stars about 1 from 7 towards 15: one of 
them is probably 8. They are equal, 12 . 8 . 8. 

1014 There is a larger star than either 10 or 14, between but following these two, 
which is not in FLAMSTEED. 

12 Appears two small for 7m. It is 8 or 9m. FLAMSTEED has no observation 
of 12. 

14 Has no time in FLAMSTEED'S observation, but it seems to be placed very justly 
in the Atlas. 

15 Eequires PD - 10'. 

16 19 There is a large star between 16 and 19 not in FLAMSTEED. The mistake of 
Sept. 14, 1795, is owing to the large above-mentioned star. 

18 There are seven stars about the place of 18. FLAMSTEED has no observation 

of 18. 

19 . 20 Sept. 14, 1795, I suppose this to be a mistake of the star. 
24 Requires + 10' or 2| in RA. 

Notes to Vulpecula. 

Vulpecula in Atlas is laid down so confusedly and erroneously that it is impossible 
to ascertain the stars without a fixed instrument. 

2 Is misplaced. It requires a correction of | minus in HA and 30' + in PD. 

3 The observation of Sept. 17, 1795, 6-3,3 Cygni does not agree with this 
3 _ _ 3 Cygni [i.e., of this date, Nov. 3, 1795]. Nov. 15, 1795, 3 - - 3 Cygni. 

7 Requires a correction, near f in RA. 

11 10- -11, but 11 is very small and FLAMSTEED has no observation of it. I 
suppose therefore that this is not the star which is given in Atlas and catalogue. 

11 is forgot in Atlas. 

13 9 - 10 , 13, Sept. 17, 1795, but 13 is further from 10 and nearer to 14 than it is 
marked in Atlas. 

12 Is placed too far north in Atlas at least 15' by 12 Sagittse. Large star in 
the breast near 14-9. 

13 The expression 10 , 13, Sept. 17, 1795, cannot be right; it is 13 - - 10. 
Dec. 4, 1796, I have my doubts about the expression 10 , 13 used Sept. 17, 1795. I 
could hardly mistake the star 10 as [? and] there is none in the neighbourhood that 
exceeds 13. 

14 A large star in Atlas preceding 14 is not in the heavens, nor do I know how it 
comes into the Atlas, as FLAMSTEED has it nowhere. This constellation must be 
reviewed again, when it is higher. 

16 A considerable star near 16. 

24 25 A star larger than either, north of 24, observed by FLAMSTEED, p. 64, is in 
ts place. 
31 32 Are contrary iu magnitude to what they are in Atlas. 



424 



DE. HERSCHEL'S SIXTH CATALOGUE OF THE 



CATALOGUE VI. 
A SIXTH CATALOGUE OF THE COMPAEATIVE BRIGHTNESS OF THE STABS. 



Lustre of the Stars in Canes venatici. 


1 




6 


5--1.7 


2 




5 


10. 2 


3 




6 


3,7 


4 




6 


9 . 4 


5 




6 


5-- 1 875 , 14 


6 




5 


8 -, 6 , 10 


7 




7 


1,7 3, 7-, 11 


8 




4.5 


25-8 8 -, 5 876 


9' 




C.7 


10, 9. 4 


10 




6 


10, 9 6, 10. 2 


11 




6 


7 -, 1 1 Note 


12 




2.3 




13 




4.5 


41 Com Ber , 13 (= 37 Com Ber) 


14 




5 


5, 14 


15 




6.5 


15. 17 


16 




6 


17 - 16 


17 




6 


15 . 17 - 16 


18 




6 


19- 18 


19 




7 


23 . 19 - 18 Note 


20 




6 


20- 23 


21 




6 


24-21 


22 




6 


Does not exist 


23 




7 


20 - 23 . 19 


24 




5.6 


24-21 


25 




5 


25-8 Note 



COMPARATIVE BRIGHTNESS OF THE STARS. 



425 



Lustre of the Stars in Coma Berenices. 


1 




7 


2.1,3 


2 




6 


5,2.1 


3 




6 


1,3 


4 




6 


13, 4 


5 




6 


5 , 2 Note 


6 




5 


6, 11 


7 


h 


4.5 


14 . 7 -, 8 7-20 24 . 7 


8 




7 


7-8 20 , 8 25 , 8 


9 




6 


9 . 10 


10 




6 9 . 10 


11 




4.5 


6,11 


12 


e 


5 


15 , 12 . 16 


13 


f 


4.5 


17 . 13, 4 


14 


b 


4.5 


16 . 14 . 17 14 . 7 


15 


C: 


4.5 


15 , 12 


16 


a 


4.5 


12 . 16 . 14 


17 


8 


4.5 


14 . 17 . 13 


18 




5 


21, 18 --22 18.26 


19 




6 


Does not exist 


20 




G 


7 - 20 , 8 


21 


9 


5 


23- 21 , 18 


22 




7 


18 --22 


23 


k 


4 


23-21 


24 




5 


24 . 7 24 ~ , 27 


25 




6 


25, 8 


26 




5 


18.26 


27 




5 


24 = , 27 , 29 27 , 36 


28 




6 


29-28 



VOL. CCV. A. 



3 I 



426 



DE. HERSCHEL'S SIXTH CATALOGUE OF THE 



Lustre of the Stars in Coma Berenices continued. 


29 




5 


27 , 29 - 28 Is the same with 36 Virginia 


30 




6 


31 , 30 


31 




4.5 


41 . 31 , 30 


32 




7 


38 , 32 . 33 


33 




7 


.32 . 33 


34 




5 
4.5 


Docs not exist 


35 




35 - - 39 Note 


36 




5 


27 , 36 - 38 


37 




5.6 


41 , 37 or 13 C;m venut 


38 




G 


36 - 38, 32 


39 




5 


35 - - 39 39 , 40 


40- 




6 


39 . 40 


41 




5.4 


43 -, 41 . 31 42 -, 41 41 , 37 Note 


42 




4.5 


5 Boot , 42 , 4 Boot 43 , 42 -, 41 Note 


43 




5.4 


43 -, 41 43 , 42 


Lustre of the Stars in Libra. 


1 




5.6 


Docs not exist Sec note 


2 




7 


2-96 Yirginis Note 


3 




6 


55 Hyd -, 3 55 Hyd -73. 14 


4 




6 


54 Hyd - 4 4 . 56 Hyd 4 is 53 Hyd 


5 




6 


5 . 18 5 . 10 


6 




5 


45 . 6 . 7 6-54 Hyd 6 is 58 Hyd 


7 


F 


5 


6 . 7 . 21 7 , 19 7-- 15 


8 




6 


24-8-25 


9 


a 


2 


27 , 9 - 20 27 . 9 - 20 27 -, 9 


10 




6 


5-10 


11 




6 


105 Virg- 11 



COMPARATIVE BRIGHTNESS OF THE STARS. 



427 









Lustre of the Stars in Libra continued. 


12 




6 


12 , 55 Hyd 


13 


e 


6 


15 , 13; 18 


14 




6 


3. 14 23, 14 


15 


? 


6 


7-- 15, 13 


16 




5.6 


16 , 105 Virginia 


17 




7 


18 . 17 


18 




6 


13 ; 18 . 17 5 . 18 19 . 18 


19 


8 


4.5 


44 . 19 . 43 31 , 19 7 , 19 19 . 18 


20 


r 


3 


20 ,40 -20 , 51 49 11yd - 20 - 38 


21 


v l 


5 


7 . 21 . 41 21 -, 22 21 - 26 


22 


i/ 2 


6 


21 -, 22 26 , 22 


23 




7 


23 , 14 Note 


24 


t i 


4.3 


48 , 24 , 37 24-8 


25 


!? 


G 


8 - 25 25 , 28 


26 




6 


21 - 26 , 22 


27 


ft 


2 


27 , 9 27 . 9 27 -, 9 27 , 24 Serpcutis Note 


28 




6 


25 , 28 


29 


O 1 


7 


32 , 29 . 34 


30 


2 


6 


33 , 30 


31 





4 


37 , 31 . 35 37 , 31 , 19 37 . 31 


32 


f 1 


6 


32 ,34 32 , 29 


33 


f 2 


7 


35 - 33 , 30 


34 


<? 


6 


32 , 34 . 35 29 . 34 


35 


4 


4 


31 . 35 . 44 34 . 35 - 33 


36 




6 


40 -, 36 


37 




6 


24 , 37 , 31 37 ,31 37 . 31 Note 


38 


7 


3.4 


39 . 38 . 51 51 , 38 , 46 20 - 38 51 . 38 38 -, 46 


39 




4 


40 , 39 . 38 46 . 39 , 40 39 ; 40 



3 I 2 



428 



DR. HERSCHEL'S SIXTH CATALOGUE OF THE 









Lustre of the Stars in Libra continued. 


40 




4 


20 , 40 , 39 39 ,40 39 ; 40 -, 36 


41 




6 


21 .41 47 , 41 


42 




6 


1 Scorp - 42 - 4 Scorp 


43 


K 


4 


19 . 43 . 45 43 , 45 


44 


/ 


4 


35 . 44 . 19 48 , 44 48 , 44 44 , 49 


45 


A 


4 


43 . 45 . 6 45-47 43 , 45 T 47 


46 





4 


51 . 46 , 48 88 , 46 . 39 4G , 48 46 - 48 38 -, 46 -, 48 


47 




6 


45 - 47 45 7 47 , 41 


48 


* 


4 


46 , 48 ,24 48 , 15 Scorp 46 , 48 , 44 46 - 48 , 44 46 -, 48 - - 49 


49 




G 


48 - - 49 44 , 49 


50 




6 


42 Sorpii - 50 50 - 43 Sorpentis 


5t 


4" 


4.5 


38 . 51 . 46 20 , 51 ,38 51 . 38 








Lustre of the Stars in Lupus. 


1 




5 


5, 1 


2 


<5 


5.0 


2,5 


3 


7 


5.6 


5 -, 3 , 4 


4 




5.6 


3,4 


5 


A 


5 


5 -, 3 2,5,1 








Lustre of the Stars in Piscis austrinus. 


1 




5 


See Note 


2 




6 




3 




6 




4 




4.5 




5 




6 




6 




6 




7 




6 





COMPARATIVE BRIGHTNESS OF THE STARS. 



429 



Lustre of the Stars in Piscis austrinus continued. 


8 




4.5 


41 Cap -, 8 


9 


i 


4 


10-9 


10 


6 


4 


10-9 


11 




6 


13, 11 


12 


7 / 


5 


12-14 12 - 1G 


13 




6 


14- 13, 11 


14 


M 


4 


14 .15 14- 15 12- 14-, 13 


15 




5.6 


14 . 15 14- 15 


16 


X 


4.5 


12 - 10 


17 





3 


17 - 22 


18 





3.4 


88 Aquar - 18 . 86 Aquar Note 


19 




5 


23-, 19 , 21 20- 19 


20 




G 


20- 19 


21 




6 


19, 21 


22 


7 


5 


22 . 23 17 - 22 


23 


8 


5 


22 . 23-, 19 


24 


a 


1 


8 Peg , 24 , 44 Peg 44 Peg is 19 Aquar Note 


Lustre of the Stars in Scorpius. 


1 


b 


6 


2,1-3 1-42 Libra 


2 


A 1 


5 


5-2-, 3 2-4 2,1 


3 


A 2 


7 


2 -, 3 4,3 1-3 


4 




6 


2-4,3 42 Lib - 4 


5 


P 


4 


5-2 


6 


7T 


3 


8-6 23 , 6 , 20 


7 


s 


3 


21 -7,8 7-8 7 ; 8 8.7 


8 


|8 


2 


7,8- 20 7-8 7 ; 8 8.7 7 ; 8 -, 6 



430 



DR. HERSCHEL'S SIXTH CATALOGUE OF THE 









Lustre of the Stars in Scorpius continued. 


9 


i 


5 


9-10 14 , 9 7 10 14. 9 , 10 


10 


CO 2 


5 


9-10 9 7 10 9 , 10 


11 







19-11 17,11 


12 


1 





13 - 12 


13 


o 2 


G 


13- 12 


14 


V 


4 


14,9 14,20 14.9 


15 


X 


5 


15 , 10 


10 




6 


15 , 10 . 18 Note 


17 







17 , 11 


18 




4 


10 . 18 


19 . 







19-11 22,19 24,19 


20 


(T 


5 


, 20 


21 


a. 


1 


21 , 50 Cyg a Cyg - - 21 -, a Ophiuchi Note 


22 




5.0 


22 , 19 22-7 25 


23 


T 


4 


23 , G 42 Oph , 23 


24 







24, 19 


25 







22 - - 25 Note 


20 





3 


14 , 26 - - 27 26 , 9 Oph Note 


27 







26 - - 27 9 Oph - -, 27 


28 







33 , 28 


29 




6 


30.29,31 29 , 38 Oph (= 31) 


30 




6 


30. 29 


31 




0.7 


29,31 29, 38 Oph (= 31) 


32 







33 .32 32 - 50 Oph 


33 




7 


33 , 1 Sagitt 33 .32 33 , 28 


34 


V 


4 


35 -, 34 


35 




3 


35 -, 34 



COMPARATIVE BKIGHTNESS OF THE STABS. 



431 









Lustre of the Stars in Serpens. 


1 




7 


4,. 1,2 


2 




7 


1,2 


3 




6.7 


3, 5 


4 




6 


6,4.1 4-, 8 4. 11 


5 




6 


5 , 10 3,5 


6 




6 


10-6 , 4 6 . 16 


7 




7 


9-7 


8 




7 


4-, 8 


9 




6 


20 , 9 - 7 


10 




6 


10-34 5 , 10 - 6 


11 






4 . 11 - 14 25-11 


12 


T 1 


7 


12 , 17 


13 


8 


3 


13-, 27 13.37 


14 


Ai 


6 


11 - 14 


15 




6 


22- 15 


16 




7 


6 . 16 


17 




6.7 


19 -, 17 12 , 17 Note 


18 


T 2 


6 


41 , 18 


19 


T 3 


6 


19- 17 26-19- 29 


20 


X 


6 


20, y 


21 


1 


5 


35 , 21 - - 22 21 -, 44 


22 




6 


21 --22 - 15 


23 


* 


6 


34, 23 


24 


a 


2 


27 Lib , 24 , 27 Here 


25 


A3 


6 


25 - 36 25 - 11 


26 




6 


26 - 19 26 , 31 


27 


X 


4 


13 -, 27 


28 


P 


3 


28 , 37 28 , 41 



432 



DK. HERSCHEL'S SIXTH CATALOGUE OF THE 









Lustre of the Stars in Serpens continued. 


29 




5.6 


19-29 


30 




6 


36 - 30 50 , 30 


31 


V 


6 


26 , 31 ; 39 


32 


1* 


4 


32 - 37 


33 




6 


Does not exist 


34 


(0 


6 


34 , 23 10 - 34 


35 


K 


4 


35 , 21 


36 


/; 


6 


25 - 36 - 30 36 , 50 


37 


e 


3 


37 . 10 Oph 32 - 37 28 . 37 - 41 13 . 37 


38 


p 


4.3 


44 , 38 


39 




6 


31 : 39 


40 




7 


46 - 40 . 45 


41 


7 


3 


10 Oph - 41 37 - 41 28 , 41 , 18 


42 




6 


Does not exist Note 


43 




6 


50 Lib - 43 


44 


TT 


4 


21 - 44 , 38 


45 




6 


40 . 45 


46 




6 


46 - 40 40 7 47 


47 




6 


467 47 


48 




6 


8 Here ; 48 48 -, 49 


49 




6 


48 - 49 


50 


IT 


5 


36 , 50 , 30 


51 




6 


51 , 25 Oph 


52 




6 




53 


V 


4 




54 




6 


47 Oph - - 54 


55 


$ 


4 




56 


o 


5 


56 -, 57 Oph 



COMPAEATIVE BRIGHTNESS OF THE STARS. 



483 



Lustre of the Stars in Serpens continued. 


57 


c 


3 


57 - 69 Oph 57 -, 69 Oph 


58 


V 


3 


58 - 64 Oph 


59 


8 


6 


59 -, 61 


60 





6 


61 . GO 60 -, 47 Oph 


61 


e 


6 


59 -, 61 . 60 


62 




6 


64-62 


63 





3 




64 




6 


64 - 62 Note 


Lustre of the Stars in Serpentarius (or Ophiuchus), 


1 


8 


3 


35 . 1 , 13 35 , 1 . 13 GO - 1. 1-13 


2 





3.4 


13,2 13-2-10 


3 


V 


5 


3 , : : 18 Lib Note 


4 


^ 


5 


4-5 87477 


5 


g 


5 


4-5-9 


6 




6 


Does not exist 


fj 


X 


6 


477 


8 


* 


4 


874 


9 


OJ 


5 


26 Scorpii , 9 - -, 27 Scorpii 5-9 


10 


A 


4 


37 Serpentis .10-41 Serpentis 2-10 


11 




6 


21 , 11 


12 




6 


19, 12 


13 


c 


3 


1 , 13 1 , 13 13, 2 13-2 1-13 Note 


14 




6 


21 , 14 , 19 


15 




6 




16 




6 


19 . 16 


17 




6 


Is 43 Herculis 


18 




6.7 


22 . 18 



VOL. CCV. A. 



3 K 



434 



DE. HEESCHEL'S SIXTH CATALOGUE OF THE 



Lustre of the Stars in Serpentarius (or Ophiuchus) continued. 


19 




6 


14,19.16 19,12 


20 




5.6 




21 




6 


21 ,14 21 , 11 


22 




7 


22 .28 22 . 18 


23 | 


6 




24 




7 


24-26 


25 


i 


4 


51 Serpentis , 25 


2G 




6 


26 -, 28 24 - 26 Note 


27 


K 


4 


[A number of comparisons of 27 with a (64) Herculis have been printed in 
the 2nd of these papers on the " Lustre of the Stars " see ' Phil. Trans.,' 
1796, p. 492 and it is needless to repeat them here. There are others, of 
27 with S (65) Here, and with GO (ft) Serpentarii. The former may be 
represented by 27; 3 Here and 8 Here; 27. For the latter, see below, 
line 60. -J. H.] 


28 




6 


26 -, 28 .31 22 . 28 


29 




6 




30 




6 


Note 


31 




6 


28 . 31 


32 




6 


32 , 33 


33 




6 


32 , 33 , 34 


34 




G 


33 , 34 


35 


n 


3 


35 . 1 35 , 1 


36 


A 


6.5 


44 , 36 , 51 


37 




6 


66 Here , 37 66 Here - 37 


38 




6-7 


29 Scorp , 38 (or 31 Seorpii) 


39 




6 


39 ;51 


40 


p 


4 




41 




G 




42 


e 


4.3 


42 - 50 Lib 42 , 23 Scorp 


43 




4.5 





COMPARATIVE BRIGHTNESS OF THE STARS. 



435 



Lustre of the Stars in Serpentarius (or Ophiuchus) continued. 


44 


B 


5.4 


44 -, 51 44 , 36 


45 




6 




46 




6 


Does not exist Note 


47 




6 


60 Serpentis -, 47 - - 54 Serpentis 


48 




6 


Does not exist 


49 


<r 


5 


67-49 


50 




7 


32 Scorp - 50 


51 


e 


6 


51-3 Sagitt 44 -, 51 39 ; 51 36 , 51 


52 




6 


2 Sagitt ,52 58 - 52 ; 2 Sagitt 


53 




6 




54 




6 


54, 56 


55 


a. 


2 


55 , a. Corona; 55 - - 60 55 , 5 Coronas 55 - 33 Drac 
a Cygni - - 55 - a Coronas a Scorp -, 55 y x Corona; 


56 




6 


54, 56 


57 


P 


4 


56 Serpentis -, 57 Note 


58 


D 


6 


58-52 


59 




6 


Does not exist 


60 


ft 


3 


60 - a Here (3 times) 60 7 a Here (3 times) 60 . 27 (y8) Here 
60 , ft Here (twice) 55 - - 60 60 , 17 Aquilse 60-1 60727 
60 .27 27 , 60 60 - - 62 Note 


61 




6 


66 , 61 


62 


y 


3 


60 - - 62 , 67 72 7 62 72 7 62 62 7 72 72 ,62 72 - 62 -, 71 
64-62 


63 




5 




64 


V 


4 


58 Serpentis - 64 - 62 


65 




6 


65-6 Sagittarii 


66 


n 


4.5 


68 , 66 , 61 66 , 73 


67 





4 


62 , 67 , 70 67 - 49 72 ; 67 


68 


k 


4 


70 , 68 , 66 



3 K 2 



436 



DR. HERSCHEL'S SIXTH CATALOGUE OF THE 



Lustre of the Stars in Serpentarius (or Ophiuchus) continued. 


69 


T 


5 


57 Serpentis - 69 57 Serpentis -, 69 


70 


P 


4 


67 , 70 , 68 


71 


s 


6 


72-71 72-, 71 62-71 


72 


s 


6 


72-71 72-, 71 72762 72762 62 7 72 ; 67 72,62 Note 


73 


2 


6 


74 ,73 66 , 73 


74 


r 


6 


74 , 73 


Lustre of the Stars in Ursa major. 


1 


4.5 


1 -, 23 1 , 69 


2 


A 


5 


3,2,4 2,5 


3 


^ 


5 


3,2 14 , 3 


4' 


1T~ 


6 


2,4.6 5,4 


5 




5 


2,5,4 


6 




5 


4. 6 


7 


I 


6 


7 is lost 


8 


l> 


5 


13 . 8, 11 


9 


i 


4 


9-25 


10 


n 


4 


39 Lyncis , 10 


11 


(T 1 


5 


8, 11 


12 


K 


4 


41 Lyncis - 12 , 39 Lyn 33 - 12 


13 


0-2 


5 


13. 8 


14 


T 


5 


14,3 14,16 24-14 


15 


/ 


5 


15 , 18 15 - 24 30 . 15 -, 18 


16 





5 


14,16 16 --,20 


17 




5 


18- 17 


18 


e 


5 


15 , 18 - 17 26 -, 18 15 -, 18 -, 31 


19 




6 


8 Leo min -19,7 Leo min 


20 


7 


16 - -, 20 Does not exist Note 



COMPARATIVE BRIGHTNESS OF THE STARS. 



437 



Lustre of the Stars in Ursa major -continued. 


21 




6 


Does not exist Note 


22 




7 


27 -22 


23 


h 


4 


1 -, 23 . 29 


24 


a 


4.5 


24-14 15-24 


25 


e 


3.4 


25 . 41 Lync 9 - 25 - 69 


26 




5.6 


30-, 26 -, IS 


27 




6 


27 - 22 


28 




5 


Does not exist 


29 


V 


4 


23 . 29 29 15 Lyncis 


30 


<; 


5 


30 -, 26 30 . 15 


31 




6 


18 -, 31 


32 




5 


32 . 38 


33 


X 


3.4 


34 -, 33 - 12 52 -, 33 - 63 


34 


p 


3 


34 -, 33 34 - 52 Note 


35 




6 




36 




5 


36 - 37 45 - 36 


37 




5 


36 - 37 -, 39 37 , 44 


38 




5 




39 




6 


37 -, 39 , 43 39 , 42 


40 




6 


41 - 40 


41 




6.7 


43 - 41 -, 40 


42 




5-6 


39 , 42 


43 




6 


39 , 43 - 41 


44 




6 


37 , 44 . 45 


45 


ia 


4.5 


44.45-36 45-55 


46 




6 


46 -, 47 Leo min 


47 




6 

! 


47 . 49 



438 



DR. HERSCHEL'S SIXTH CATALOGUE OF THE 



Lustre of the Stars in Ursa major continued. 


48 


|8 


2 


50 - _ 48 79 - 48 . 64 79 -, 48 .64 48 7 64 (twice) 64 ; 48 
48 - 64 (3 times) 


49 




6 


47 . 49 - 51 


50 


a 


1.2 


50 - 77 (5 times) 50 - - 48 50 7 77 (twice) 50 ; 77 50 f 77 
50 77 77 , 50 85 | 50 77 50 , /3 Urs min 50 '. /3 Urs min 
50 f 7 (/?) Urs min Note 


51 




7 


49-51 


52 


# 


3.4 


34 - 52 -, 33 


53 


$ 


4 


63 - 53 


54 


i' 


4 


54 - 63 


55 




5 


45 _ 55 55 - 67 


56 




6 


56 -, 59 57 . 56 


57 




6 


57 . 56 G7 - 57 


58 




6 


59 , 58 58 . 60 


59 




6 


56 -, 59 , 58 61 . 59 , 62 


60 




6 


65 ,60 58 . 60 


61 




6 


61 . 59 


62 




6 


59 , 62 


63 


X 


4 


33 - 63 54 - 63 - 53 


64 


7 


2 


48 . 64 -, 69 48 , 64 ~ ~ - 8 or 69 48 7 64 7 Urs min - 64 
64 ; 48 48 -, 64 48 - 64 (3 times) 


65 




7 


65 , 60 


66 




6 


71.66 70.66 


67 




6 


55 _ 67 - 57 


68 




7 


70 - - 68 73 - 68 . 72 


69 


3 


2.3 


69 -, 70 69-74 1 , 69 64 -,69 64 = - - 69 25 - 69 


70 




6 


69 -, 70 - - 68 75 . 70 . 71 74 , 70 . 75 70 771 70 . 66 


71 




7 


70.71.73 71.66 70771.73 


72 




7 


73 -, 72 73 - 72 68 . 72 



COMPARATIVE BRIGHTNESS OF THE STARS. 



439 



Lustre of the Stars in Ursa major continued. 


73 




6 


71.73-, 72 71.73-72 73-68 


74 




6 


69 - 74 , 75 74 ,70 76 - 74 76 . 74 


75 




6 


74,75.70 70.75 Note 


76 




6 


76 . 76 - 74 Note 


77 





3 


77 ,85 50 - 77 (3 times) 50 7 77 ; 85 50 ; 77 (3 times) 50 -, 77 
50 ;' 77 - 79 50 ; 77 77 ,50 77 7 85 77-79 1 Urs min . 77 


78 




6 


78 ; 80 Note 


79 


f 


3 


85 , 79 - 48 79 | 7 Urs min 77 - 79 -, 48 


80 


9 


5 


83 , 80 , 81 80 ,83 78 ; 80 


81 




5.6 


80 ,81 84 , 81 . 86 83 , 81 . 84 


82 




6 


86 . 82 Note 


83 




6 


87 - 83 , 80 83 ,84 80 , 83 , 81 


84 




6 


83 , 84 , 81 81 . 84 . 86 


85 


n 


3 


77 , 85 , 79 77 ; 85 , 79 85 | 50 77 ; 85 


86 




6 


81 .86 84 . 86 . 82 Note 


87 




5 


87-83 87-8 Draconis 


Lustre of the Stars in Virgo. 


1 


0) 


6 


4-1 2,1 2-1,4 


2 


' 


5 


8-2-4 4-2,1 2-11 2-1 8,2 


3 


V 


5 


9_3_8 9-3-8 9,3-8 


4 


2 


6 


2-4-1 4-2 1,4-6 


5 


/8 


3 


43 , 5 - 15 43 , 5 - 15 


6 


A 


6 


43 - 6 . 109 4-6 7,6 12 ; 6 


7 


b 


5.6 


8-7 7. 13 7,6 7-, 10 7-11 7 , 13 


8 


TT 


5 


3_8-2 3-8-7 9-8,16 3-8,2 8-16 51 ; 8 - 78 


9 


O 


5 


9-3 9-3 9-8 9,3 


10 


r 


6 


12-10 7-, 10 11,10 10-17 



440 



DR. HERSCHEL'S SIXTH CATALOGUE OF THE 









Lustre of the Stars in Virgo continued. 


11 


s 


6 


2-11-12 7 - 11 , 10 


12 


f 


6.7 


11-12-10 12.17 12:6 


13 


n 


6 


7 . 13 7 , 13- 14 


14 




6 


13- 14 


15 


>} 


3 


5 - 15 15 - 51 15 - 93 109 . 15 , 107 5 - 15 


16 





4.3 


8,16 8-16 


17 




6 


12 .17 10 - 17 




18 




6 


Does not exist Note 


19 




6 


Does not exist Note 


20 




6 


27 .20 27 . 20 


21 


'/ 


6 


26 - 21 , 25 


22 




6 


27 .22 31 . 22 Does not exist Note 


23 




6 


Does not exist Note 


24 




G 


Does not exist Note 


25 


./' 


6 


21 , 25 -, 28 Note 


26 


X 


5 


26-21 


27 




6 


33 , 27 27 . 22 27 .20 30 - - 27 . 20 33 , 27 - - 42 (see note) 
41-, 27 


28 




6 


25 - 28 


29 


7 


3 


47 - 29 - 79 67 - 29 . 47 29 , 47 


30 


P 


5 


30-32 30 - - 27 30 , 32 


31 


8 1 


6 


32 - 31 - 33 32 ,31 32 . 31 32 , 31 


32 


G 2 


6 


30 - 32 - 31 32 ,31 30 , 32 . 31 32 , 31 See note 


33 




6.7 


31 - 33 33 ,27 33 - 34 33 , 27 


34 




6 


33 - 34 36 , 34 , 41 


35 




6 


37 , 35 


36 




6 


36 , 34 


37 




6 


37, 35 



COMPARATIVE BRIGHTNESS OF THE STARS. 



441 









Lustre of the Stars in Virgo continued. 


38 




6 


48. 38 


39 




6 


40-39 40 - - 39 


40 


* 


5 


40-39 40 - - 39 


41 




6 


34 , 41 , 27 


42 




6 


27 - - 42 Note 


43 


8 


3 


79-43 79,43,5 79.43-6 47-43,5 79-43 


44 


k 


6 


46 . 44 , 48 


45 




6 


Does not exist Note 


46 




6 


46 . 44 


47 


i 


3 


67 - 47 - 29 29 . 47 - 79 29 , 47 -, 43 


48 




6 


44 , 48 . 38 


49 


ff 


5 


49 -, 50 49 - 50 


50 




6 


49 -, 50 ,52 50 , 52 49 -, 50 - - 56 


51 


6 


4 


15-51-74 51; 8 


52 




6 


50 , 52 . 62 Docs not exist Note 


53 




4.5 


53 ,61 61 - 53 , 55 


54 




6 


61 , 54 61 -, 54 73 .54 57 - 54 57 - 54 


55 




6 


55 .57 61 - 55 . 57 55 .57 53 , 55 . 57 


56 




6 


58 .56 56 , 58 50 - - 56 


57 




6 


55 . 57 - 61 55 .57 55 . 57 - 54 55 . 57 - 54 


58 




6 


62 . 58 . 56 56 , 58 Note 


59 


e 


6.7 


60 , 59 , 64 70 - 59 , 71 


60 


<T 


5 


84 - 60 - 78 60 - 64 60 , 59 


61 




4.5 


61 ,69 57 - 61 , 54 53 , 61 -, 54 61 - 55 61 - 53 Note 


62 




6 


62 . 58 52 . 62 


63 




6 


697 63 


64 




6 


60 - 64 59 , 64 


65 




6 


74 - 65 . 66 



VOL. CGV. A. 



3 L 



442 



DR. HERSCHEL'S SIXTH CATALOGUE OF THE 









Lustre of the Stars in Virgo continued. 


6G 




6.7 


65 . 66 , 72 66 , 80 


67 


a 


1 


67-47 ft Gem , a. Virg . a Leon 67 - 29 67 7 -, 32 Leon Note 


68 


I 


4 


69 - 68 , 75 


69 




5.6 


69 -, 68 61 -, 69 7 63 


70 




6 


70-59 




71 




6 


59 , 71 Note 


72 


P 


6 


80 - 72 66 , 72 . 80 70 -, 72 - 77 80 , 72 82 - 72 - -, 77 


73 




6 


73. 54 


74 


P 


6 


51 _ 74 _ 80 74 - 65 74 -, 82 


75 




6 


68, 75 


76 


h 


/> 


82 . 76 -, 72 76 - 80 


77 




7 


72 - 77 , 81 72 - -, 77 . 81 


78 




6 


60-78 8-78 -, 84 


79 


i 


6 


29 - 79 - 43 79 ,43 47 - 79 . 43 79 - 43 


80 


p 


6 


74 - 80 - 72 72 .80 76 - 80 66 , 80 , 72 


81 




6 


77,81 77.81.88 Note 


82 


m 


6 


74 -, 82 .76 82 - 72 


83 




6 


89 , 83 , 87 Note 


84 





6 


93 _ 84 _ 60 78 -, 84 


85 




6 


87 ,85 86 , 85 


86 




6 


87 . 86 , 85 


87 




6 


83 , 87 , 85 87 . 86 


88 




6 


81 . 88 Note 


89 




5.6 


89 , 83 


90 


P 


6 


93 - - 90 , 92 


91 




6 


Does not exist 


92 




6 


93 - 92 90 , 92 


93 


r 


5 


15 _ 93 _ 84 93 - 92 107 . 93 . 99 93 - - 90 



COMPAKATIVE BRIGHTNESS OF THE STARS. 



443 









Lustre of the Stars in Virgo continued. 


94 




6 


95 , 94 - 97 94 , 96 


95 




6 


98 -, 95 , 94 


96 




5 


94 , 96 , 97 2 Lib - 96 


97 




6 


94 - 97 96 , 97 


98 


K 


4 


99 - 98 . 100 98 -, 95 98 , 100 98 ; 110 


99 


I 


4 


93 . 99 - 98 107 -, 99 Note 


100 


A 


4 


98 . 100 98 , 100 110; 100 


101 




6 


20 Bootis -, 101 Note 


102 


V 1 


5 


105 - 102 -, 103 102 - 104 


103 


tf 


5 


102 -, 103 106 , 103 


104 




6 


102 - 104 . 106 104 , 108 


105 


4> 


4 


105- 102 16 Lib, 105-11 Lib 


106 




6 


104 . 106 , 103 


107 


V- 


4 


15 , 107 . 93 107 -, 99 109 - 107 


108 




6 


104 , 108 


109 




4 


6 , 109 . 15 109 - 107 


110 




6 


98; 110; 100 



3 L 2 



444 DR. HERSCHEL'S SIXTH CATALOGUE OF THE 

Notes to Canes venatici. 

July 22, 1797. 11 There are two stars about the place of 11 nearly alike in 
brightness. 

13 Is 37 Comae Berenices. 

19 A considerable star sp 19 is omitted : much larger than 18. 

22 Does not exist. It was never observed by FLAMSTEED. 

25 Is misplaced: the PD should be +10. It is not in the place where the 
catalogue has it, but is 10 more south. 25 - 8 A star observed by FLAMSTEED, 
p. 228, is in its place about f or 1 north of this 25, and a little preceding it is 
* , 14. 

A star observed by FLAMSTEED, p. 225, from 64 Ursae towards 54 Ursse is in its 

place. It is 1 7 * 

Notes to Coma Berenices. 

5 December 27, 1786. I looked for 5 Comae, but could not find it. 
19 April 19, 1797. 19 does not exist. FLAMSTEED never observed it. 
29 Is the same with 36 Virginis. 

34 Does not exist, nor did FLAMSTEED observe it. 

35 39 A star between 35 and 39 observed by FLAMSTEED, p. 165, is in its place. 
It is 39 =, * 

41 A star near 41 observed by FLAMSTEED, p. 165, is in its place. A star south 
following 41 observed by FLAMSTEED, p. 165, is in its place. It is 41 - - * 

42 A star south of 42 observed by FLAMSTEED, p. 164, is in its place. Calling it 
in general * it will be 38 , * 

Notes to Libra. 

1 Does not exist : there is a star of a considerable magnitude near 50 Hydrse, but 
the place does not agree with 1 1 is not in the place where it is marked in Atlas, 
but there is a star which FLAMSTEED observed, p. 166, which is probably 1. It is 
RA-30' and PD + 2 and is in its place. I shall call it 1 and it is 50 Hydrae -, 1 

2 There are two about the place of 2, but I suppose the largest, and nearest to 
98 Virginis, to be FLAM STEED'S star. It agrees best with the place. 

23 Is not in the place where Atlas gives it, nor did FLAMSTEED observe it there. 
He has a star, p. 531, which is 1 26' more in EA. This is probably 23, and it is 
23 , 14 and is in its place. 

27 Does not seem larger than 9, at least not very decidedly, and so as to be 
denoted 27 , 9, but 9 has a small star near it, not visible to the naked eye, which 
increases its lustre ; but in my glass it is evident that 27 is a little brighter than 9. 

37 North of 37 is a star nearly as large as 37, but 37 is a very little larger in the 
finder. -FLAMSTEED'S star observed, p. 45, north of 37 is in its place 37 - * 



COMPARATIVE BRIGHTNESS OF THE STARS. 445 

Note to Piscis austrinus. 

September 22, 1795. This constellation, on account of its low situation, can be of 
no use for comparative magnitudes. The opportunities of observing it must be so 
scarce that no discoveries of changes can be made in it. I can see no other star with 
the naked eye but those I have equated [viz., 24 and 18. The observations of other 
stars of this constellation were made two years later. J. H.]. 

Notes to Scorpius. 

16 Should be about 3 or 4 minutes nearer to 15. FLAMSTEED'S observation, p. 197, 
leaves the ZD doubtful. 

21 Is of a very brilliant ruddy light. Is of a pale garnet colour : it seems to be 

the most coloured of all the large stars. Its low situation probably contributes to it. 

25 Either does not exist or is misplaced. There is a star about 4 from 23 and 
2f from 22, which may be the star if misplaced. In that case the RA of 25 should 
be 1 and it will be 22 7" 25. Several stars of Serpentarius are so small that 25 
may exist. 

26 Being low it may be larger than 14, for I make no allowance in my 
observations. 

Notes to Serpens. 

17 There are two of 17 but little different in brightness. I have taken the 
brightest of them. 

33 Does not exist. FLAMSTEED never observed it. 

42 Does not exist. The place where it should be, according to the catalogue, 
cannot be mistaken. FLAMSTEED never observed it. 50 Libra? not far from it is in 
its place. 

(63) = I Aquila3 and less than X Aquilae. 

64 Is the largest of two. 

Notes to Serpentarius (Ophiuchus). 

3 (u) is misplaced in Atlas 1. It should be about +1 in RA. A star f north of 
it, observed by FLAMSTEED, pp. 442, 443, is in its place. 

6 Does not exist. FLAMSTEED never observed it. 

13 3 np 13 is a star not marked in FLAMSTEED = 20. 

26 28 26 has another near it larger than 28. 

30 Seems not to be rightly placed. 

38 31 Scorpii is 38. 

46 A larger star than 46 is just by, but not marked in Atlas. 46 does not 

exist. 



446 DK. HERSCHEL'S SIXTH CATALOGUE OF THE 

48 Does not exist. FLAMSTEED never observed either of them. 

57 A large star np 57 observed by FLAMSTEED, p. 442, is in its place. It is 57 * 

59 Does not exist. FLAMSTEED never observed it. 

60 I suspect 27 Herculis to be changeable, for it is now 60 . 27 Here, or even 
27 Here , 60. There is great difference in the weather. 

72 Is much too large for 6m. 

Notes to Ursa major. 

20 There is a very small star about the place of 20, which I can hardly take for 

one of FLAMSTEED'S. It is 16 - -, 20. 20 does not exist in the place where it is 

marked in the Atlas. There is no star but of the 9th mag. within a degree of 

the place. 

21 I think does not exist. There is a star not far from the place where the Atlas 
has it, but it is much too small. 21 does not exist. I cannot mistake the place. 

34 The star south of 34 observed by FLAMSTEED, p. 439, is in the place. 

35 Is not as laid down in Atlas. 

50 a (Oct. 25, 1795) Appears unusually large 8 h - 20-. When I saw it at 6 h - I 
thought so immediately. I suspect it to be changeable, or rather am pretty sure it is 
so. It is as large as /8 Ursse minoris, but that is so much higher that no fair 
comparison can be made between them. 

Oct. 26, 1795. 50 is not so bright as last night. 

Oct. 28, 1795. It is much less than it was Oct. 26. The place of the moon may 
possibly influence appearances. 

Nov. 28, 1795. It would not be proper to compare Urs. maj. with e and 17, as 
they are much lower, but a seems to be remarkably bright. 

75 Has no time in FLAMSTEED'S observations and is misplaced in Atlas. It is but 
very little following 74, being almost in the same RA with it. 

76 There are two of 76, at a distance of nearly |- from each other. 

77 June 25, 1796, 77 is very bright. July 21, 1796, 77 is decreased. 

78 Is missing; at least is not as marked in Atlas. 78 has no time. In the 

observation of FLAMSTEED in the Atlas, it is placed about 20' of a degree too 
far East. 

82 Is missing. 

86 The place of 86 is not right in Atlas by many minutes, perhaps 15'. 

Notes to Virgo. 

18 Is lost. 18 does not exist, or is reduced to 9m at least. 18 does not exist. 

19 Is lost ; or, as there are 4 or 5 stars about its place, if it is among them, it is at 
least reduced to the 10th mag. 19 exists not, or is less than 9m. There are 3 or 
4 stars near the place, but extremely small. 19 does not exist, or is at least 9m or 



COMPARATIVE BRIGHTNESS OF THE STARS. 447 

10m. 19 exists not, but there is a star sp 20 about the same distance as 19 is 

marked np. 

22 Is in its place and 7m. 22 23 are both either 7 or 7 . 8 mag. 22 does not 

exist. The observation 31 , 22, April 9, 1796, can not be right. I mistook very 

probably a star sf 32 and 31 instead of np, as there is such a one. 22 and 23 do 

not exist. FLAMSTEED has no observation of them. There is a pretty considerable 

star near the place of 22. 23 is not to be seen. There is no star that can be 

taken for it. 23 does not exist. There is no star that can be taken for it. 

24 is lost. There is no small star to represent it. 24 does not exist. There is 

no star that can be taken for it. 24 does not exist. FLAMSTEED has no observation 

of it. 

25 By FLAMSTEED'S observations requires 19' in RA and by the heavens it does 
the same. 

42 Does not exist. There is no star nearer than 1 of any size to the place of 
42 given in Atlas. FLAMSTEED never observed this star. The star estimated 

April 9, 1796, 27 42 is one of these small stars nearest the place, which is rather 

larger than 2 or 3 others thereabout. 

45 I cannot see 45. There is no star so large as 10 or llm near the place of 45. 
45 does not exist. FLAMSTEED never observed it. 

52 Does not exist. There is a very small star not far from the place. FLAMSTEED 
has no observation of 52. 

58 The PD of 58 should be +11'. 58 by FLAMSTEED'S observations requires 
+ 11' in PD and by the heavens it does the same. 

56 58 They are very small stars. 58 is double in my finder. There are two other 
stars situated like 56 and 58 in Atlas, which were probably taken for them, 
May 2, 1796, when they were estimated 58 . 56. Not knowing then that 58 wants 
a correction of PD + ll', occasioned the mistake. 

61 There seems to be a change in the brightness of 61 since last night. 

67 Is of a sparkling bluish white colour : a beautiful star. 

71 A star following 71 observed by FLAMSTEED, p. 194, 478 [sic] is in its place 
* . 71 59 , * . 71. 

77 . 81 . 88 The three last are very small stars. About the place of 88 there are 
two nearly equal. I cannot determine which is FLAMSTEED'S star. 

83 The RA of 83 should be +22' by FLAMSTEED'S observations, and it requires the 
same by the heavens. 

91 Does not exist. 

99 The star nf 99 observed by FLAMSTEED, p. 41, is in its place. It is 108 * 

101 Is misplaced in the British Catalogue : it should be +1 in PD. Then it is 
20 Bootis -, 101. 



[ 449 ] 



XIII. On the Accurate Measurement of Ionic Velocities, with Applications to 

Various Ions. 

By R. B. DENISON, M.Sc., Ph.D., and B. D. STEELE, D.Sc, 
Communicated by Sir WILLIAM RAMSAY, K.C.B., F.R.S. 

Received October 14, Read November 16, 1!)05. 

ACCORDING to ARRHENIUS' theory of electrolytic dissociation, the conduction of the 
current in a salt solution is due to the presence of free ions, which, Tinder the 
influence of an electromotive force, move towards the electrodes with a velocity 
depending, other conditions being equal, upon the magnitude of the driving force, or 
fall of potential. This "ionic velocity" can be determined by means of two quite 
distinct methods, of which one may be termed the indirect and the other the direct 
method. The former, or indirect method, was evolved by KOHLRAUSCH on his 
recognition of the law of the independent migration of the ions, which he thus states : 
" The molecular conductivity, p, of a solution is proportional to the sum of the 
velocities of the anion and of the cation, p. = constant x (u + v)." 

The ratio of these velocities, u/v, had been determined many years previously by 
HITTORF, whose " Uberfuhrungszahl," or transport number, p = u/(u + r), for any salt 
represents the fraction of the total current that is carried by the anion. 

The knowledge of this ratio enabled KOHLRAUSCH to calculate the ionic velocities 
from the molecular conductivity. In order to calculate the velocities of the ions 
by the indirect method it is, therefore, necessary to know both the molecular 
conductivity of the solution and its transport number. Although the determination 
of the former is perfectly easy and straightforward, that of the latter by HITTORF'S 
analytical method is both difficult and laborious, and the method suffers from the 
great disadvantage that the success or failure of an experiment is known only after 
the necessary chemical analyses have been completed. 

In recent years a method of measuring transport numbers and ionic velocities has 
been worked out in which the actual rate of motion of the ions is read off by means 
of a scale and telescope. The first steps in this direction were taken in 1886 by 
LODGE (' British Assoc. Reports,' 1886, p. 389), whose idea was to make the invisible 
ion indicate its presence by some characteristic physical or chemical property, such as 
its colour or the formation of a precipitate with some other ion. For the gradual 

VOL. CCV. A 399. 3 M 12.3.06 



450 DE. E. B. DENISON AND DE. B. D. STEELE ON THE 

development of this idea reference must be made to the original literature ;* but the 
following is a brief account of the method in its present form : 

It has been shown, both theoretically and experimentally, that if two salt solutions 
containing a common ion are placed one above the other, and an electric current 
passed through the system, a stable margin will be formed between the two solutions, 
provided that the specifically slower non-common ion follows the faster one. Under 
these circumstances it has been shown that the boundary moves in the same direction 
as the non-common ions and measures their velocity. In order to observe and measure 
the velocity of the boundary, advantage is taken of the slight difference in the 
refractive index of the two solutions, which difference renders the margin quite 
visible when viewed through a telescope. The method of determining the ratio U/V, 
and hence the transport number. U/(U + V), for a given salt will be rendered clear by 
the following considerations :- 

Let us suppose that a current flows through the system, 

Anode solution of lithium chloride solution of potassium chloride solution of 
potassium acetate cathode. 

At the margin between the lithium and potassium chloride solutions the slower 
lithium ion follows the specifically faster potassium ion, and there results a stable 
margin, the velocity of which is that of the lithium and potassium ions at that point. 
This, velocity, however, depends on the potential gradient, and it has been proved 
that the concentration of the lithium chloride becomes automatically adjusted, so that 
the potential gradient is just sufficiently increased to make the lithium ions keep pace 
with the potassium ions. In the same way the specifically slower acetate ion follows 
the faster chlorine ion, at the margin potassium acetate, chloride, and the motion of 
this margin gives the velocity of the acetate-chlorine ions ; but whilst the lithium 
and acetate ions are moving under the influence of an unknown potential gradient, 
that which is driving the potassium ion is the same as that driving the chlorine ion 
the potassium chloride solution being homogeneous and, therefore, the velocities of 
these two ions are strictly comparable. Moreover, the potential gradient in the 
middle electrolyte can easily be calculated, and hence, also, the average mobility of 
the ions, or their velocity under a driving force of one volt per centimetre. 

The ratio U/V and the average mobilities of the ions of a number of salts have 
been determined in this way,t and whilst the agreement between the results so 
obtained and those obtained by the indirect method is, on the whole, fair, considerable 
deviations occur in the case of many salts. In the method used for these measure- 

* WHETHAM ('Phil. Trans.,' A, 1893, p. 337; A, 1895, p. 507); MASSON ('Phil. Trans.,' A, 1899, 
p. 331); KOHLRAUSCH (' Wied. Ami.,' 1899, LXII., p. 209); WEBER ('Sitz. Berliner Akad.,' 1897); 
STEELE ('Phil. Trans.,' A, 1902, p. 105; 'Zeit. fiir Phys. Chem.,' 1902, XL., p. 689); ABEGG and GAUS 
('Zeit. fur Phys. Chem.,' 1902, XL., p. 737); DENISOX ('Zeit. fiir Phys. Chem., 1 XLIV., p. 575). 

t MASSON (he. tit.) STEELE (loc. tit.). 



ACCURATE MEASUREMENT OF IONIC VELOCITIES, ETC. 451 

ments the solution to be measured was separated from the solutions containing the 
slower indicator ions by two partitions of a gelatine solution of the same indicators, 
and in this way it was possible to place the solutions in position without any 
appreciable mixing taking place at the surfaces of contact. 

It has been shown by DENISON (loc. cit.) that the deviations referred to are due, 
largely, if not entirely, to the occurrence of electric endosmose at the gelatine 
partitions. DENISON measured the amount of endosmose, and applied the correction 
to the ratio U/V with satisfactory results in the case of many salts. 

The present research has been undertaken with the object of devising a method by 
means of which the solutions could be superposed without mixing, and which would 
avoid the use of membranes of any sort during the progress of the experiment. 

The use of gelatine especially was to be avoided, not only on account of electric 
endosmose, which would be caused by any membrane, but also on account of the ease 
with whicli it melts on the passage of even small currents, and on account of the 
impossibility of obtaining it free from saline impurities. Even the purest obtainable 
gelatine contains a quantity of saline matter which is an appreciable fraction of the 
concentration of a moderately dilute salt solution, and this is probably the reason 
why our previous attempts to measure such solutions have been unsuccessful, and it 
appears to be impossible to measure transport numbers in dilute solutions in a system 
containing gelatine. Now we know that it is only in the case of the simple salts of 
the alkali metals that the transport number is practically independent of concen- 
tration ; with other salts the general tendency is for the anion transport number to 
increase with increasing concentration. This gives, of course, different values for the 
velocity of the same ion at different dilutions, and, moreover, the velocity of one and 
the same ion is found to be different for the same concentration when measured in 
different salts. These differences, however, vanish in dilute solution* in which, in 
accordance with the theory of KOHLRAUSCH and ARRHENIUS, a given ion has the 
same velocity in different salts. Hence an extension of the direct method of 
measuring ionic velocities to dilute solutions is much to be desired on account of its 
great simplicity and ease of manipulation. 

Before this could be accomplished, however, it was necessary to devise some means 
of observing the margins. If gelatine be employed as membrane, the margins become 
invisible in solutions more dilute than about 0'2 N. 

It was thought that an electrical method could be used to indicate the position of 
the boundary by taking advantage of the difference in conductivity of the indicator 
and measured solutions. This method, however, proved impracticable. Coloured 
salt solutions could not be used as indicators, as in solutions of about 0'02 normal the 
colour of solutions of salts such as copper sulphate, cobalt sulphate, nickel sulphate, &c., 
is much too faint to be serviceable. The intensely coloured ions of some of the 
organic dyes were tried, but, although certain acid dyes are excellent anion indicators, 
* STEELK and DENISON, ' Journ. Chem. Soc.,' 1902, LXXXL, p. 456. 

3 M 2 



452 



DE. R. B. DENISON AND DR. B. D. STEELE ON THE 



no basic dye was found sufficiently free from hydrolysis to be of any use as a cation 
indicator. It was ultimately found that, by the use of very high voltages, distinctly 
visible refraction margins could be obtained in solutions as dilute as 0'02 N. 

Method of Experiment. 

The placing of the two indicator solutions in contact with the middle electrolyte 
without appreciable mixing taking place, and without using gelatine or other 
membrane during the experiment, presented considerable difficulty. The ordinary 
method of pouring the one solution upon a thin piece of cork floating on the other 
solution was found to be quite unsatisfactory. The problem was finally solved by 
the use of the apparatus shown in figs. 1 and 2. It consists of two parts which are 



\ 





Fig. 1. 




Fig. 2. 



joined together at G or G'. If both indicators are lighter than the solution to be 
measured, the apparatus is made up of two halves of the form shown in fig. 1. If 
both are heavier, then both halves are of the form shown in fig. 2. If one indicator 



ACCURATE MEASUREMENT OF IONIC VELOCITIES, ETC. 453 

is lighter and the other heavier than the solution to be measured, one-half of the 
form of fig. 1 and one-half like fig. 2 are used in constructing the apparatus. 

In fig. 2 a hole with a collar is shown in the bottom of the thermostat H. The 
apparatus can be passed through this hole and held in position by a rubber ring, L. 
This was found to be the best way of supporting this half of the apparatus. Both 
forms of the apparatus consist essentially of three tubes, an electrode vessel, E or E', 
a vessel, B or B', containing the indicator solution, and the tubes A or A' in which 
the boundaries move. The tubes A and A' are made from carefully selected glass 
quill-tubing of about 4 to 5 millims. diameter, and are accurately calibrated. They 
are sealed into the wider tubes B or B' in such a manner that they form a shoulder 
projecting inwards. The lower extremity of the capillary tube K is expanded into 
a cone, C, around which a piece of parchment paper can be tightly stretched. This 
parchment paper fits over the projecting shoulder, so that when pressed upon it there 
is no mixing of the liquid poured into the apparatus through the tube K with the 
liquid previously placed in A. The tubes K and K' slide easily through holes in 
rubber corks, so that after an electrolytic margin has appeared in the tubes A or A' 
the membrane can be withdrawn from the shoulder, and a free passage is allowed for 
the current. The cones C are provided with holes to allow the passage of the liquid 
into B and also to permit the free flow of the electric current when the membrane is 
resting on the projecting shoulder. 

The choice of electrodes and electrode solutions needs careful consideration if 
accurate results are to be obtained. It is obvious that no gas evolution at the 
electrodes must occur if a good margin is to be maintained. The indicator solutions 
most frequently employed were lithium chloride and sodium acetate, and in all our 
experiments the cathode consisted of lead wire dipping into and completely covered 
by a paste of lead peroxide, which completely prevented any evolution of hydrogen. 
The anode consisted of a copper wire dipping into cadmium amalgam, thus con- 
stituting a completely unpolarisable electrode. A rough calculation showed that the 
total volume change at the electrodes corresponding to the changes 

PbO 2 +H 2 = Pb + 2H 2 O and Cd+2Cl = 



was negligible. To prevent the hydroxyl ions formed at the cathode from finding 
their way back into the middle electrolyte, the cathode was surrounded with a 
solution containing acetic acid. 

The cadmium chloride formed at the anode is to some extent hydrolysed, and the 
hydrogen ions thus formed travel towards the cathode across the cation margin and 
decrease the resistance of the solution there, and so also the fall of potential and the 
velocity of the margin. To prevent this, a little sodium or lithium hydroxide was 
added to the solution surrounding the cadmium electrode. If these precautions were 
neglected, slightly false values for the transport numbers were obtained. 

The whole apparatus was held in position by means of a hinged wooden arm, and 



4 54 DK. R. B. DENISON AND DR. B. D. STEELE ON THE 

placed in a bath with plate-glass sides. The framework of the bath was of copper and 
provided with flanged edges, on which the plate-glass sides were clamped. Rubber 
tubing was placed between the copper flanges and the glass, and in this way a perfectly 
water-tight junction was made and the use of putty rendered unnecessary, a con- 
siderable advantage if the bath is to be heated. The base of the bath was provided 
with two holes for the insertion and support of the apparatus shown in fig. 2. 

In putting together the apparatus for an experiment, the electrode vessels E are 
first filled and the electrodes placed in position, care being taken that none of the 
electrode liquid passes over into B or A.* The two halves of the apparatus are then 
connected by rubber tubing and the tubes A are filled just to the shoulder with the 
solution to be measured. The rubber cork carrying the tube K and the membrane is 
then placed in position! and pressed on the shoulder, care being taken not to 
imprison any air-bubbles below the membrane. The electrical connections having 
been made, the current is started by pouring the indicator through F (fig. 1) or L 
(fig. 2), after which the plugs P and P' are inserted. The appearance of the margins 
in the tubes generally occupies only a few minutes, and as soon as they have 
advanced about 1 centim. into the tubes the membranes are removed by lifting K or 
lowering K'. In this manner electric endosmose is entirely prevented. The velocities 
of the two margins are measured by observing the distance moved in stated intervals 
of time, the observations being made by means of a telescope with cross wires and a 
glass scale placed immediately behind the tubes A and A'. 

One other point requires notice. The tubes K in apparatus fig. 1 and P' in 
apparatus fig. 2 must not have a greater diameter than about 1 millim. The reason 
for this is as follows : Suppose that we are measuring the transport number of 
sodium chloride with lithium chloride and sodium acetate as indicators, both solutions 
being lighter than that of sodium chloride. In one measuring tube we have the 
solutions lithium chloride over sodium chloride, and in the other sodium acetate over 
sodium chloride, and the relative length of the columns of lithium chloride and 
sodium acetate depends on the position of the margins. Now the sodium ion travels 
more slowly than the chlorine ion, with the result that a longer column of sodium 
acetate than of lithium chloride is formed. These solutions have different densities, 
and so there is a difference of hydrostatic pressure tending to move the whole column 
of liquid up one measuring tube and down the other, and the level in the tubes K 
and P becomes slightly altered during the progress of the experiment. This change 
of level accelerates one margin and retards the other, and false values for the 
velocities and transport number are obtained. In order to reduce the effect of the 
change of level, the diameters of K and of P are made as small as possible, and hence, 
since the total change of level amounts to only a fraction of a millimetre, the 

* In the final form of apparatus the two halves were sealed together. 

t In the case of the apparatus (fig. 2) used for heavy indicators, the tube K is placed in position before 
putting the solution into the tube A. 



ACCtTKATE MEASUEEMENT OF IONIC VELOCITIES, ETC. 



455 



movement of the margin in the measuring tubes A due to this cause is infinitesimal 
and can be neglected. In our earlier experiments, in which the apparatus was tested 
with potassium chloride, the wide tubes B were open to the atmosphere, but as the 
potassium and chlorine ions have practically the same velocity, the effect described 
above did not manifest itself. But with n/10 sodium chloride the introduction of the 
capillary tubes K changed the transport number for chlorine from 0'58 ( J to its correct 
value, 0'614. 

The electrical connections and the method of illuminating the boundary are the 
same as those described in_ previous papers.* 

Testing the Method. 

The only difficulty in the present method has been found to lie in the choice of 
suitable indicators. The transport number of any ion in a given salt should be the 
same at the same concentration, provided that the indicator used fulfils certain 
conditions, which are briefly as follows : 

(1) The specific velocity of the indicator ion must be less than that of the ion 
whose progress it indicates. 

(2) It must not react with any of the ions of the -salt being measured, nor must it 
be hydrolysed or give rise to any other ion moving in the same direction as the 
indicator ion. 

(3) The resistance of the indicator solution must not be too great, -i.e., the 
concentration of ions in the indicator must not be too small, nor must there be too 
great a difference between the specific ionic velocity of the indicator ion and that of 
the ion whose velocity is being measured. 

The method was first tested by measuring the transport numbers of potassium and 
sodium chlorides with different indicators, and the following results (Table 1.) were 

obtained : 

TABLE 1. 



Salt and 
concentration. 


Indicator ions. 


Anion transport 
number p. 


HITTOUF'S value t 


i KC, { 


Li and acetate 
,, formate 


0-508 
0-513 


0-514 


y Nad { 


acetate 
,, formate 


0-614 

0-621 


0-637 


ft KC1 { 


,, acetate 
formate 


0-508 
0-508 


| 0-508 


re N C1 { 


acetate 
formate 


0-017 
0-618 


0-617 



* STEELE, loo. dt. DENISON, loc. at. 

t From KOHLRAUSCH and HOLBOKN'S ' Leitrermogen der Electrolyte,' p. 201. 



456 DR. K. B. DENISON AND DR. B. D. STEELE ON THE 

These results show that the method is capable of great accuracy. There is, indeed, 
a slight difference between the values of the transport numbers for the normal 
solutions according as acetate or formate is used as anion indicator, the percentage 
difference being about the same with potassium chloride as with sodium chloride. 
Although there is only a small difference between HITTORF'S value for these solutions 
and that found by us with sodium acetate, it is too large to be attributed to errors of 
experiment. We have measured these solutions repeatedly, and with the utmost 
precautions, and invariably obtain results which lie between 0'508 and 0'510 for 
potassium chloride and between 0'613 and 0'615 for sodium chloride. It is, therefore, 
necessary to recognise the presence of some unknown disturbing factor in these 
experiments. Whatever this factor is, its effect has disappeared in the more dilute 
solutions, and for these accordingly we have continued to use sodium acetate as anion 
indicator. For stronger solutions, however, it is advisable to use sodium formate. 

Sodium benzenesulphonate lias been successfully employed by us as aiiion indicator 
in some experiments, but when it is used for stronger solutions thann/10, irregularities 
occur, the cause of which we have not yet succeeded in tracing. 

Experimental Result*. 

We have measured the transport number and ionic velocities of those salts only 
which give rise to strong ions, that is, salts which undergo little or no hydrolysis in 
aqueous solution. 

The necessity of paying attention to the possibility of hydrolysis in all electrolytic 
experiments cannot be too strongly emphasised. Thus, it is of no value to determine 
the velocity of the ions of a salt which, when dissolved, gives rise to a complicated 
ionic system. We cannot assume, a priori, that the transport number of any ion as 
determined by the present method will give us the true fraction of the total current 
which is carried by that ion in the presence of other ions of the same sign. In 
HITTORF'S analytical method the actually measured transport number gives us the 
fraction of the total current carried by the ion in question, whether complex ions are 
present or not, if we assume that the current is wholly carried by the simple ions. 
Whether the direct method, and the method of HITTORF, will give the same transport 
number for a given ion in more complex ionic systems, or whether the presence of 
complex ions in solutions will affect the results obtained by the two methods to a 
different extent, are subjects for future experimental and mathematical investigation. 

By means of the present method we have been enabled to obtain for the first time 
an experimental determination of the transport number for such salts as potassium 
chlorate, bromate and perchlorate, which present considerable difficulty in the 
determination by the analytical method. 

In the following Table II., which contains the results of our transport-number 
determinations, the values given in the last column are taken from KOHLRAUSCH and 
HOLBORN'S ' Leitvermogen der Electrolyte.' The salts used were obtained from 
KAHLBAUM and were not submitted to any further purification. 



ACCURATE MEASUREMENT OF IONIC VELOCITIES, ETC. 

TABLE II. 



457 



Salt. 


Concentration. 


Indicator. 


Anion 

transport 
number. 
V/(U + V). 


KOHLRAUSCH. 


Cation. 


Anion. 


KC1 


0-ln 

0-02 
0-02 


Lithium 


>> 
)> 


Formate 
Acetate 
j> 
Benzenesulphonate 


0-513 
0-508 
0-507 
0-507 


0-514 
0-508 
0-507 
0-507 


NaCl 


0-ln 

0-05 
0-04w 


F| 

J> 
) 

)! 


Formate 

Acetate 

n 
11 


0-621 
0-618 
0-614 
0-612 


0-637 
0-617 
0-614 


BaCI, 


0-7n 
0-ln 

0-02 


1) 

T> 



j 

ij 


0-624 
0-580 0-585 
0-565 0-565 


SrCl 2 


0-ln 
0-02 


J) 
I) 


u 

jj 


0-601 
0-589 





CaCla 


0-lw 

0-02 


! 

)) 




;i 


0-602 
0-588 


0-64 
0-59 


KNOs 


0-ln 
0-02 


J) 

) 


j) 

i? 


0-498 
0-498 


0-497 


K 2 S0 4 


0-lw 

0-02n 




I! 


j> 
?) 


0-515 
0-512 





KC10 3 


O-l/i 
0-02 


)) 
>J 


) 

!) 


0-464 
0-466 





KBr0 3 


0-ln 

0-02 


)? 
II 


JJ 
JJ 


0-430 
0-433 





KC10 4 


0-lw 


) 


JJ 


0-477 





KBr 


0-lw 
0-02 



J) 


JJ 
JJ 


0-519 
0-518 


0-507 
0-507 


KI 


In 
0-02 


J) 

JJ 


JJ 
JJ 


0-514 
0-513 


0-507 
0-507 


KOH 


1-Ow 
0-ln 


J) 

51 


Bromide 

jj 


0-738 
0-743 


0-735 


NaOH 


1-0 
0-lM 



J 


u 

jj 


0-839 
0-842 


0-82 
0-81 


HC1 


0-lw 
0-02w 


Potassium 
i) 


lodate 

u 


0-165 
0-165 


0-172 


HN0 3 


0-ln 
0-02n 


ii 

j 


u 
jj 


0-145 
0-154 





H 2 S0 4 


0-lw 
0-02n 


jj 



u 
u 


0-172 
0-167 


0-191 



VOL. CCV. A. 



3 N 



458 DR. R B. DENISON AND DE. B. D. STEELE ON THE 

It will be seen from the table that our results agree excellently with those 
obtained by HITTORF'S method, the difference in most cases being only a few units in 
the third decimal place. One of the most marked exceptions is n/l sodium chloride, 
for which we find 0'621 instead of 0'637. We have repeated this experiment a 
number of times and always with the same result. Possibly the older value requires 
confirmation. 

KOHLRAUSCH and HOLBORN give the same value, 0'508, for the anion transport 
number of potassium chloride, bromide, and iodide. On the other hand, we have 
found the following values : 

Potassium chloride, p = 0'508. Potassium bromide, p = 0'518. 
Potassium iodide, p = 0'513. 

As these results were so different from what we expected, we have measured the last 
two salts several times and invariably with the same result, so that we were at last 
convinced that our numbers were correct. We have since found a paper by 
KOHLRAFSCH (' Zeit, fur Electrochemie,' 1902, VIII, p. 630) which had escaped our 
notice. In this paper KOHLRAUSCH describes experiments showing that the velocities 
of the ions Cl', Br', and P, as determined from conductivity measurements, are as 

follows : 

Cl = 65-44. Br = 67'63. I = 60'40. 

These figures give for the transport number of the three salts the following 

numbers : 

Potassium chloride = 0'502, Potassium bromide = 0'511, and 
Potassium iodide = O'SOl, 

which is practically the same ratio as that found by us. The difference between the 
actual values is due to KOHLRAUSCH'S figures being for infinite dilution, whereas ours 
are for n/50 solutions. 

Further confirmation of the correctness of our results is afforded by the fact, which 
will be referred to again later, that the potassium ion has the same velocity in 
equimolecular solutions of the above three salts if our values for the transport 
numbers are correct, but its velocity is different if the ordinary values are correct. 

Measurement of the Ionic Velocities. 

The terra " ionic velocity " appears to have been used by different writers in 
different senses, and as a consequence there is some confusion as to its exact 
significance. In what follows we shall speak of: 

(1) The actual measured velocity of the ion or ionic margin, which is its velocity 

under the potential gradient of the experiment. 

(2) The actual mobility (U or V) or the velocity of the ion in a given solution 

under a potential gradient of 1 volt per centimetre. 



ACCUEATE MEASUREMENT OF IONIC VELOCITIES, ETC. 459 

(3) The specific mobility (u or v) or the velocity which the ion would have under 

a potential gradient of 1 volt per centimetre if the salt were completely 
dissociated. These are related to the actual mobilities as follows : 

U = au and V = av, 

a being the degree of dissociation of the salt. 

(4) The " lonen Beweglichkeit " (l a or l k ) of KOHLRAUSCH, which is given by the 

relation 



p. being the molecular conductivity. 

The use of the term " specific ionic velocity " for l a and l k is confusing, 
and we suggest instead the name " specific ionic conductivity." 
(5) The " ionic conductivity " for a given strength of solution can then be 
conveniently represented by 

L re and L k , where L,, = a/,, and L* = //,. 

The actual mobilities U and V are obtained from the measured velocities In- 
dividing the latter by the potential gradient in the measuring tube. This potential 
gradient, II, is easily calculated as follows : According to OHM'S law the current, C, 
flowing through the apparatus, C = H/>: C is measured, and /, or the resistance of 
1 centim. of the liquid, is obtained from its specific conductivity, K, and the area of 
cross-section, A, of the tube, v = 1/*A and hence IT = C/A. 

The actual mobilities of the ions of a number of salts have been measured, and the 
results at 18 are contained in Columns 6 arid 9 of Table III, and, for comparison with 
these, two sets of figures are given in Columns 7 and 10 and 8 and 11 respectively. 
These figures are calculated from KoHLRAUSCH's conductivity data in the following 



&> 
manner : 



The molecular conductivity 

^ 
whence 



K = 



t) being the concentration in gramme equivalents per cubic centimetre. 

Now, K is the specific conductivity, or the quantity of electricity carried in one 
second between two electrodes 1 centim. apart in a tube of 1 sq. ceutim. cross-section 
under a potential gradient of 1 volt per centimetre. 

This obviously depends on (a x rj), or the number of ions present, on their specific 
mobility (u and v), and on the quantity of electricity carried by one gramme ion, viz., 
96540 coulombs. Hence 

K = 7?(-t-v) 96540 = 17 (U + V) 96540, 
3 y 2 



460 



DK. R. B. DENISON AND DR. B. D. STEELE ON THE 



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ACCURATE MEASUREMENT OF IONIC VELOCITIES, ETC. 
and from these two equations we obtain 



461 



= (L a +L,)x 



96540' 



and 



u + v = 



96540- 



We thus obtain the value of (U + V), and by multiplying this by the anion transport 
number U/(U+V) we obtain U and, consequently, V also. 

It will be noticed that the figures given in columns 7 and 10 agree on the whole 
much better with the directly observed mobilities than do those given in columns 8 
and 11. In calculating the former our transport number has been used, those ot 
KOHLRAUSCH having been used in calculating the latter. The two sets of transport 
numbers are given in columns 4 and 5. 

The comparison can be made in the opposite manner, p. being calculated from the 
actual mobilities from the relation 



p. = 



= a(u + v) x 96540 = (U + V) x 9G540. 



This calculation has also been made and the results are given in the second column of 
the table, KOHLRAUSCH'S values for ^ being given in the third column. 

Table IV. contains a similar set of results to those given in Table III., the 
measurements having been made at 25 with 10"' normal solutions. As conductivity 

TABLE IV. 



1. 


2. 


3. 


4. 


5. 


6. 


7. 


8. 




T = 25 C. 




Anion velocity, V. 


Cation velocity, U. 


Salt. 


Molecular 


Molecular 


Transport 
number, 












con- 
ductivity, 


con- 
ductivity, 


V/(U + V). 


Found. 


Calculated. 


Found. 


Calculated. 




fj., from 


H, KOHL- 














U + V. 


RAUSCH. 












KC1 


128-2 


128-8 


0-507 


0-000674 


0-000676 


0-000654 


0-000658 


KBr 


131-9 


132-0 


0-520 


0-000710 


0-000711 


0-000656 


0-000657 


KI 


130-0 


130-9 


0-517 


0-000696 


0-000701 


0-000652 


0-000655 


KN0 3 


119-8 


119-4 


0-499 


0-000619 


0-000618 


0-000621 


0-000620 


KBr0 3 


107-7 


107-2 


0-430 


0-000480 


0-000479 


0-000636 


0-000635 


KC10 3 


113-2 


113-2 


0-463 


0-000544 


0-000544 


0-000631 


0-000631 


K. 2 S0 4 


108-9 


109-0 


0-521 


0-000588 


0-000588 


0-000540 


000540 


CaCl 2 


101-0 


101-4 


0-604 


0-000631 


0-000635 


0-000412 


0-000416 


BaCL, 


105-2 


105-2 


0-584 


0-000638 


0-000638 


0-000452 


0-000452 


SrCl 2 


101-2 


101-2 


0-596 


0-000626 


0-000626 


0-000424 


0-000424 



determinations at this temperature were not available, the calculated mobilities given 
in columns 6 and 8 were obtained from our own conductivity measurements, which 
are given in column 3 for comparison with the molecular conductivities (column 2) as 



462 



DE. K. B. DENISON AND DR. B. D. STEELE ON THE 



calculated from our specific mobilities (columns 3 and 5), whilst the agreement 
between the found and calculated values is remarkably close in the majority of 
instances. A few cases, where the differences are larger, call for special comment. 
For example, the calculated and observed mobilities of the hydrogen ion in hydro- 
chloric and nitric acid solutions agree very well indeed, whereas the agreement is by 
no means good for the velocities of the anions of these acids. This is explained by 
the fact that the velocity of the hydrogen ion is about five times as great as that of 
the chlorine ion (or nitrate ion), and as a consequence the latter only moves about 
10 millims., whilst the former moves through the whole length of the tube. The 
result of this is that there is a very much larger percentage experimental error 
introduced in the measurement of the mobility of the anion than in that of the cation 
of an acid. The same applies, but in the opposite sense, to the measurement of the 
mobilities of the anion and cation of an alkali. 

The observed values for /10 sulphuric acid are quite different from the calculated 
values. Whether this is due to the inaccuracy of the transport number, or to the 
occurrence of complexes in the system, it is not possible to say, but the cause of error 
seems to have completely disappeared in the n/50 solutions. 

Interesting results are obtained when we compare the velocities of the same ion in 
equimolecular solutions of different salts. KOHLRAUSCH'S law of the independent 
wandering of the ious depends on the assumption that, in solutions sufficiently dilute 
for any variation in " electric friction " to be neglected, the same ion has the same 
velocity in whatever solution it occurs. If this is so, and remembering that it is only 
the specific mobility, u, that is invariable, and that the actual mobility U = au, we 
see at once that it is only in solutions of salts that are equally ionised that we can 
expect to find the same actual mobility for the same ion, and, on the other hand, 
where we do find this, we have strong evidence that the salts in solution are equally 
ionised. 

On comparing the velocities of the potassium ion in equimolecular solutions of all 
the potassium salts that we have measured (see Table V.), we find that this velocity 
is identical in solutions of potassium, chloride, bromide, and iodide, but is a little 
smaller in the other solutions. This identity of mobility is manifested not only in 

TABLE V. Velocity of K ion in various Salt Solutions. 



Salt. 


/10 at 18. 


m/50 at 18. 


n/10 at 25. 


KC1 


0-00056,3 


0-000606 


0-000654 


KBr 


0-000562 


0-000598 


0-000656 


KI 


0-000564 


0-000599 


-0,00652 


KC10 3 


0-000549 





0-000631 


KBr0 3 


0-000551 


0-000601 


0-000636 


KN0 8 


0-000536 


0-000583 


0-000621 


K 2 S0 4 


0-000510 


0-000593 


0-000540 



ACCURATE MEASUREMENT OF IONIC VELOCITIES, ETC. 



463 



10 th normal solutions at 18 and 25, but also in 50 th normal solutions at 18. In the 
same way the mobilities of the chlorine ion in equimolecular solutions of different salts 
have been gathered together in Table VI. In this case, also, the same mobility 

TABLE VI. Velocity of Cl ion in various Salt Solutions. 



Salt. 


n/10 at 18. 


n/50 at 18. 


/10 at 25. 


KC1 


0-000582 


0-000622 


0-000674 


NaCl 


0-000585 








BaCl 2 


0-000554 


0-000603 


0-000638 


SrCl. 


0-000559 


0-000604 


0-000626 


CaCL, 


0-000542 


0-000596 


0-000631 



occurs in solutions of potassium and sodium chlorides, and similarly for the hydrogen 
mobilities which are given in Table VII. 

These results indicate that the direct measurement of the actual ionic mobility 
gives us a means of comparing the degree of ionic dissociation of equimolecular 

TABLE VII. Velocity of H ion in various Acids. 



Salt. 


n/10 at 18. 


./50 at 18\ 


w/10 at 25. 


HC1 
HNO 3 
H 2 S0 4 


0-00304 
0-00311 
0-00201 


0-00317 
0-00315 
0-00242 






solutions of salts containing a common ion. If we assume that in dilute solutions v, 
or the specific mobility of a given ion, is invariable in different salt solutions, then, 
since U = av, a is proportional to U. Table VIII. contains a comparison on this 
basis of the degrees of dissociation of all the salts containing one ion in common that 
have been measured by us. The figures are given as the ratio of the degree of 
dissociation of the salt to that of potassium chloride, which has been taken as 
standard, and the same ratio has been calculated from the conductivity data, and the 
results are given for comparison in the third and fifth columns of the table. 

From the very satisfactory agreement of the results obtained by the present 
method with the corresponding numbers given by KOHLRAUSCH, it is evident that a 
considerable degree of accuracy in the direct measurement of ionic velocities has been 
attained. It is interesting to look over HITTORF'S early transport numbers, amongst 
which deviations of 5 and 10 per cent, are frequently met with. 

The numbers subsequently obtained were much more concordant, but the method, 
as already stated, is difficult and laborious, and only rarely can an experiment be 



464 



ON THE ACCURATE MEASUREMENT OF IONIC VELOCITIES, ETC. 



completed in a day. The direct method, in its present form, gives results at least as 
accurate as the indirect one, and with much less trouble. In dilute solution the 
determination is generally complete in about half an hour, as the high voltage, which 
is necessary in such solutions, imparts a considerable velocity to the ions. After 

TABLE VIII. Degrees of Dissociation. 



O li 


w/10. 


n/50. 


oalt. 


Found. 


Calculated. 


Found. 


Calculated. 


KBr 


1-00 


1-00 


0-98 




KI 


1-00 


1-01 


0-98 


1-01 


KN0 3 


0-95 


0-97 


0-96 


1-00 


K,S0 4 


0-85 


0-83 


0-93 


0-91 


KC10 3 


0-98 





0-91 





KBr0 3 


0-98 





0-90 





NaCl 


1-01 


0-99 


. 





BaCla 


0-95 


0-88 


0-97 


0-93 


SrCL, 


0-96 


0-88 


0-97 


0-93 


CaCL 


0-94 


0-87 


0-96 


0-91 


HC1 


1-01 


1-07 


1-02 


1-04 


HN0 3 


1-02 


1-01 


1-01 


1-00 



becoming accustomed to the method, it is easy to perform five or six experiments in a 
day. In general the total amount of motion for anion and cation was about 
G centims., with a probable error in reading of about O'Ol centim. for each boundary, 
i.e., a total error of about 0'3 per cent. The error in measuring the conductivity 
might be - 5 per cent., and the error in measuring the small amount of current 
flowing through the apparatus also about O'o per cent. The error in the calibration 
of the tube is negligible, and, therefore, in a good experiment the transport number 
should be correct to about 1 part in 300, and the ionic velocities to at least 1 part 
in 100. As a matter of fact, this degree of accuracy is easily attainable for the 
transport number. In the case of the separate ionic velocities the accuracy obtainable 
is not quite so great owing to the accumulation of errors from the various measure- 
ments involved. 



[ 465 ] 

XIV. On Mathematical Concepts of the Material World. 

By A. N. WHITEHEAD, Sc.D., F.R.S., Felloiv of Trinity College, Cambridge. 

Keceived September 22, Head December 7, 1905. 

PREFACE. 

THE object of this memoir is to initiate the mathematical investigation of various 
possible ways of conceiving the nature of the material world. In so far as its results 
are worked out in precise mathematical detail, the memoir is concerned with the 
possible relations to space of the ultimate entities which (in ordinary language) 
constitute the "stuff" in space. An abstract logical statement of this limited 
problem, in the form in which it is here conceived, is as follows : Given a set of 
entities which form the field of a certain polyadic (i.e., many-termed) relation R, 
what "axioms" satisfied by R have as their consequence, that the theorems ot 
Euclidean geometry are the expression of certain properties of the field of R ? If the 
set of entities are themselves to be the set of points of the Euclidean space, the 
problem, thus set, narrows itself down to the problem of the axioms of Euclidean 
geometry. The solution of this narrower problem of the axioms of geometry is 
assumed (cf. Part II. , Concept I.) without proof in the form most convenient for this 
wider investigation. But in Concepts III., IV., and V., the entities forming the field 
of R are the " stuff," or part of the " stuff," constituting the moving material world. 
POINCARE* has used language which might imply the belief that, with the proper 
definitions, Euclidean geometry can be applied to express properties of the field 
of any polyadic relation whatever. His context, however, suggests that his thesis 
is, that in a certain sense (obvious to mathematicians) the Euclidean and certain 
other geometries are interchangeable, so that, if one can be applied, then each of 
the others can also be applied. Be that as it may, the problem, here discussed, is 
to find various formulations of axioms concerning R, from which, with appropriate 
definitions, the Euclidean geometry issues as expressing properties of the field of R. 
In view of the existence of change in the material world, the investigation has to 
be so conducted as to introduce, in its abstract form, the idea of time, and to provide 
for the definition of velocity and acceleration. 

The general problem is here discussed purely for the sake of its logical (i.e., 
mathematical) interest. It has an indirect bearing on philosophy by disentangling the 
essentials of the idea of a material world from the accidents of one particular concept. 
The problem might, in the future, have a direct bearing upon physical science if a 
concept widely different from the prevailing concept could be elaborated, which 
* Cf. ' La Science et 1'Hypothese,' chap. III., at the end. 

VOL. COV. A 400. 3 16.5.06 



466 DR. A. N. WHITEHEAD ON 

allowed of a simpler enunciation of physical laws. But in physical research so much 
depends upon a trained imaginative intuition, that it seems most unlikely that 
existing physicists would, in general, gain any advantage from deserting familiar 
habits of thought. 

Part I. (i) consists of general considerations upon the nature of the problem and 
the method of procedure. Part I. (ii) contains a short explanation of the symbols 
used. Part II. is devoted to the consideration of three concepts, which embody the 
ordinary prevailing ideas upon the subject and slight variants from them. The 
present investigation has, as a matter of fact, grown out of the Theory of Interpoints, 
which is presented in Part III. (ii), and of the Theory of Dimensions of Part IV. (i). 
These contain two separate answers to the question : How can a point be defined in 
terms of lines ? The well-known definition* of the projective point, as a bundle of 
lines, assumes the descriptive point. The problem is to define it without any such 
assumption. By the aid of these answers two concepts, IV. and V., differing very 
widely from the current concepts, have been elaborated. Concept V., in particular, 
appears to have great physical possibilities. Indeed, its chief difficulty is the 
bewildering variety of material which it yields for use in shaping explanations of 
physical laws. It requires, however, the discovery of some appropriate laws of motion 
before it can be applied to the ordinary service of physical science. 

The Geometry throughout is taken to be three-dimensional and Euclidean. In 
Concept V. the definition of parallel lines and the " Euclidean " axiom receive new 
forms ; also the " points at infinity " are found to have an intimate connection with 
the theory of the order of points on any straight line. The Theory of Dimensions is 
based on a new definition of the dimensions of a space. 

The main object of the memoir is the development of the TJieory of Interpoints, of 
the Theory of Dimensions, and of Concept V. The other parts are explanatory and 
preparatory to these, though it is hoped that they will be found to have some 
independent value. 

PART I. (i) GENERAL CONSIDERATIONS. 

Definition. The Material World is conceived as a set of relations and of entities 
which occur as forming the " fields " of these relations. 

Definition. The Fundamental Relations of the material world are those relations 
in it, which are not defined in terms of other entities, but are merely particularized 
by hypotheses that they satisfy certain propositions. 

Definition. The hypotheses, as to the propositions which the fundamental relations 
satisfy, are called the Axioms of that concept of the material world. 

Definition. Each complete set of axioms, together with the appropriate definitions 
and the resulting propositions, will be called a Concept of the Material World. 

* Here in "Descriptive Geometry" straight lines are open, and three collinear points have a non- 
projective relation of order ; in " Projective Geometry " straight lines are closed, and four collinear points 
have a projective relation of separation. 



MATHEMATICAL CONCEPTS OF THE MATERIAL WORLD. 467 

Definition. The complete class of those entities, which are members of the fields 
of fundamental relations, is called the class of Ultimate Existents. This technical 
name is adopted without prejudice to any philosophic solution of the question of the 
true relation to existence of the material world as thus conceived. 

Every concept of the material world must include the idea of time. Time must be 
composed of Instants (cf. BERTRAND EUSSELL, ' Mind,' N.S., vol. 10, No. 39). Thus 
Instants of Time will be found to be included among the ultimate existents of every 
concept. 

Definition. The class of ultimate existents, exclusive of the instants of time, will 
be called the class of Objective Reals. 

The relation of a concept of the material world to some perceiving mind is not to 
be part of the concept. Also we have no concern with the philosophic problem ol 
the relation of any, or all, of these concepts to existence. 

In Geometry, as derived from the Greeks, the simple elements of space are points, 
and the science is the study of the relations between points. Points occur as 
members of the fields of these relations. Then matter (the ultimate " stuff" which 
occupies space) in its final analysis, even if it is continuous, consists of entities, here 
called particles, associated with the points by relations which are expressed by 
saying that a particle occupies (or is at) a point. Thus matter merely occurs as one 
portion of the field of this relation of occupation ; the other portion consists of points 
of space and of instants of time. Thus " occupation " is a triadic relation holding in 
each specific instance between a particle of matter, a point of space, and an instant of 
time. According to this concept of a material world, which we will call the Classical 
Concept, the class of ultimate existents is composed of three mutually exclusive 
classes of entities, namely, points of space, particles of matter, and instants of time. 
Corresponding to these classes of entities there exist the sciences of Geometry, of 
Chronology, which may be defined as the theory of time considered as a one- 
dimensional series ordinally similar to the series of real numbers, and of Dynamics. 
There appears to be no science of matter apart from its relations to time and space. 

Opposed to the classical concept stands LEIBNIZ'S theory of the Relativity of Space. 
This is not itself a concept of the material world, according to the narrow definition 
here given. It is merely an indication of a possible type of concepts alternative to 
the classical concept. It is not very obvious how to state this theory in the precise 
nomenclature here adopted. The theory at least means that the points of space, as 
conceived in the classical concept, are not to be taken among the objective reals. 
But a wider view suggests that it is a protest against dividing the class of objective 
reals into two parts, one part (the space of the classical concept) being the field of 
fundamental relations which do not include instants of tune in their fields, and the 
other part (the particles) only occurring in the fields of fundamental relations which 
do include instants of time. In this sense it is a protest against exempting any part 
of the universe from change. But it is not probable that this is the light in which 

3 o 2 



468 DR. A. N. WHITEHEAD ON 

LEIBNIZ himself regarded the theory. This theory, though at present it is nominally 
the prevailing one, has never been worked out in the form of a precise mathematical 
concept. It is on this account criticized severely by BERTRAND RUSSELL (cf. loc. tit. 
and 'Philosophy of LEIBNIZ,' Cambridge, 1900, p. 120), who, however, has gone 
further than any of its upholders to give it mathematical precision. Of course, from 
the point of view of this paper, we are not concerned with upholding or combatting 
any theory of the material world. Our sole purpose is to exhibit concepts not 
inconsistent with some, if not all, of the limited number of propositions at present 
believed to be true concerning our sense-perceptions. 

Definition. Any concept of the material world which demands two classes of 
objective reals will be called a Dualistic concept ; whereas a concept which demands 
only one such class will be called a Monistic concept. 

The classical concept is dualistic ; Leibnizian concepts will be, in general, monistic 
(cf. however Concept IV A.). OCCAM'S razor Entia non multiplicanda prseter 
necessitatem formulates an instinctive preference for a monistic as against a 
dualistic concept. Concept III. below is an example of a Leibnizian monistic concept. 
The objective reals in it may be considered to represent either the particles or the 
points of the classical concept. But they change their spatial relations. Perhaps 
LEIBNIZ was restrained from assimilating his ideas more closely to Concept III. by a 
prejudice against anything, so analogous to a point of space, moving a prejudice 
which arises from confusing the classical dualistic concept with the monistic concepts. 
It is of course essential that at least some members of the class of objective reals 
should have different relations to each other at different instants. Otherwise we are 
confronted with an unchanging world. Concept V. is another Leibnizian monistic 
concept. 

The Time- Relation, In every concept a dyadic serial relation, having for its field 
the instants of time and these only, is necessary. The properties of this Time- 
Relation form the pure science of chronology. The time-relation is, in all concepts, a 
serial relation ordinally similar to the serial relation which generates the series of 
negative and positive real numbers.* This fact need not be further specified during 
the successive consideration of the various concepts, nor need any of the propositions 
of pure chronology be enunciated. 

Definition. The class of instants of time is always denoted by T in every concept. 

The Essential Relation. In every concept at least all the propositions of geometry 
will be exhibited as properties of a single polyadic relation, here called the essential 
relation. The field of the essential relation will consist, either of the whole class of 
ultimate existents (e.g., in Concepts III., IVs. and V.), or of part of the class of 
objective reals together with the instants of time (e.g., in Concept IVA.), or of the 
whole class of objective reals (e.g., in Concept II.), or of part of the class of objective 

* For interesting reflections on this subject, influenced by the Kantian Philosophy and previous to the 
modern " Logicization of Mathematics," cf. HAMILTON, ' Lectures on Quaternions,' preface. 



MATHEMATICAL CONCEPTS OP THE MATERIAL WORLD. 469 

reals (e.g., in Concept I.). The essential relation ol any one concept will be a relation 
between a definite finite number of terms, for example, between three terms in 
Concepts I. and II., between four terms in Concept III., and between five terms in 
Concepts IV. and V.* 

Definition. In the exposition of every concept, the essential relation of that 
concept is denoted by R. 

The Extraneous Relations. In all the concepts here considered, other relations, 
here called the extraneous relations, will be required in addition to the time-relation 
and the essential relation. In Concepts I. and II. and IV. an indefinite (if not 
infinite) number of extraneous relations are required, determining the positions of 
particles. In Concepts III., IV. and V. one tetradic extraneous relation is required 
to determine the "kinetic axes" of reference for the measurement of velocity. 

The time-relation, the essential relation and the extraneous relations form the 
fundamental relations of any concept in which they occur. 

It will now be necessary to define geometry anew, since the previous definition has 
essential reference to the dualism of the classical concept. A proposition of geometry 
is any proposition (l) concerning the essential relation ; (2) involving one, and only 
one, instant of time ; (3) true for any instant of time. 

In the classical concept everything is sacrificed to simplicity in reference to 
geometry, probably because it arose when geometry was the only developed science. 
The result is that, when the properties of matter are dealt with, an appalling number 
of extraneous relations are necessary. 

Judged by OCCAM'S principle, this class of extraneous relations forms a defect in 
Concepts I. and II. and IV. Also, in both forms of the classical concept (viz., in 
Concepts I. and II.) geometry is segregated from the other physical sciences to a 
greater degree than in the other concepts. 

In the study of any concept there are four logical stages of progress. The first 
stage consists of the definition of those entities which are capable of definition in 
terms of the fundamental relations. These definitions are logically independent of 
any axioms concerning the fundamental relations, though their convenience and 
importance are chiefly dependent upon such axioms. The second stage consists of the 

* Th